The criteria here is for a key Premier League player that will be looking to improve next season, so no promoted clubs. Sorry…

Arsenal: Granit Xhaka
Why the disappointment? Whatever anyone might tell you – and plenty will on social media – Xhaka did not perform to the level Arsenal had hoped in his first season. He was expected to be the answer, and that never quite happened. Not being good at tackling did not help.
Chances of vast improvement: High, actually. If Arsenal can either provide him with a regular partner not called Francis Coquelin or buy one if Arsene Wenger feels it necessary, it’s not hard to think that Xhaka might look far better. For £33m, we hope so.

Bournemouth: Jordon Ibe
Why the disappointment? Ibe was Bournemouth’s record signing before Nathan Ake joined; this is not a club that should spend £15m lightly. Not only was he not as inventive or creative as Eddie Howe would have hoped, he dropped out of the team completely towards the end of the season. Two league starts since November tells its own story.
Chances of vast improvement: Hmmmm. Ibe will need to improve drastically to win back the Bournemouth supporters, but at 21 has plenty of time on his side.

Burnley: Andre Gray
Why the disappointment? It might sound harsh given that Gray scored nine times during his first season in the top flight, but plenty was expected of him after a successful Championship campaign. The striker was banned for historic homophobic tweets, was outscored by Sam Vokes and was actually named on the bench for eight league games.
Chances of vast improvement: 
At Burnley, slim. Gray has rejected their offer of a new contract and is a reported target for Newcastle, amongst others. Time to cash in on the accrued goodwill of that Championship goalscoring record?

Chelsea: Michy Batshuayi
Why the disappointment? Describing Batshuayi as a key player is generous, but Chelsea’s 2016/17 campaign was hardly defined by underperformance. Having been signed for £33m, he cost Chelsea £139,830 per minute last season, and I haven’t included wages. Because I’m lazy.
Chances of vast improvement: Well. Had you asked me two days ago, I would have said that Romelu Lukaku’s arrival would make things very difficult for Batshuayi. That’s not to that he’s suddenly going to get his chance, but he might be thanking Michael Emenalo’s incompetence as we speak.

Crystal Palace: Steve Mandanda
Why the disappointment? Because he was a non-entity. Mandanda joined with a glowing reputation, started nine matches (conceding 10 in his last three), got a serious injury and then basically gave up on life at Selhurst Park.
Chances of vast improvement: Slim to none. There was surprise expressed when Mandanda actually turned up for Palace’s preseason training, but his happy ending is likely to involve a move back to Marseille.

Everton: Ross Barkley
Why the disappointment? Probably the most frustrating player in the Premier League, one who has bags of ability but makes us want to climb through the television to shake him. Still, why would you take one touch when seven will do?
Chances of vast improvement: Who bloody knows. Barkley is clearly available for transfer, but at a whacking great price. If he stays he has a chance to thrive away from the shadow of Lukaku. If he leaves, another manager might be destined to tear out their hair.

Leicester City: Islam Slimani
Why the disappointment? Take your pick between Daniel Drinkwater, Ahmed Musa, Nampalys Mendy and every member of the defence, but Slimani is Leicester’s record signing, and scored five league goals after September. With Musa and Mendy possibly leaving, Slimani can stay and step up.
Chances of vast improvement: Not bad at all. The Premier League’s history is littered with players who have improved in their second seasons after settling in. What price Slimani forging a decent partnership with Jamie Vardy?

Liverpool: Nathaniel Clyne
Why the disappointment? Liverpool signed Clyne as England’s first-choice right-back and the perfect player to rampage down their right flank. He’s now firmly behind Kyle Walker for England, and some Liverpool fans were questioning his performances at time last season.
Chances of vast improvement: Good. Liverpool having a settled central defence would help, as would having Naby Keita playing on the right of a midfield three. Clyne should be licking his lips in anticipation of Liverpool getting that deal done.

Manchester City: John Stones
Why the disappointment? Like Xhaka at Arsenal, Stones was not awful but also far below the level his club would expect after such an outlay. He was supposed to be the one that improved City’s defensive inadequacies; it was them who dragged him down.
Chances of vast improvement: As good as anyone. With – hopefully – a competent goalkeeper behind him, Vincent Kompany hopeful that his injury problems are over and Pep Guardiola to buy some sensational full-backs, Stones can be the beneficiary of the improvement in those around him.

Manchester United: Henrikh Mkhitaryan
Why the disappointment? Because we saw how brilliant and beautiful Mkhitaryan was in the Bundesliga, and desperately wanted the same to happen here. There were flashes – particularly in the Europa League – but not consistent achievement.
Chances of vast improvement: Real good. Mkhitaryan’s debut Premier league season was littered by injuries and he suffered from Jose Mourinho’s sharp tongue. With a full preseason, we’re confident.

Southampton: Fraser Forster
Why the disappointment? A rotten old season. Forster began it with hopes of taking advantage of Joe Hart’s Euro 2016 nightmare, but ended it down the queue for England. If Southampton had viable backup, his place would be in danger there too.
Chances of vast improvement: Forster will hope that he can fall back into form as easily as he fell out of it. He is still under 30, after all.

Stoke City: Saido Berahino
Why the disappointment? After battling personal problems and Tony Pulis, the move to Stoke City from West Brom was supposed to give Berahino a new lease of life. So it hasn’t proved.
Chances of vast improvement: It’s all getting a little worrying. It is more important that Berahino resolves his personal issues than starts scoring again, but Mark Hughes will soon lose patience.

Swansea City: Jefferson Montero
Why the disappointment? I remember being excited when Montero came to the Premier League. He was quick and tricky, and thrived on his early outings. With 373 Premier League minutes last season, that feels a very long time ago.
Chances of vast improvement: Nada. Zilch. Zip. Montero is the subject of reported interest from Mexico, and you can’t imagine that Paul Clement will fight too hard to keep him. He’s still only 27; such a bloody shame.

Tottenham: Moussa Sissoko
Why the disappointment? I could give you 5,000 words, but let’s start with 34: Sissoko cost £30m having been close to a move to Everton and consistently talked up his love for Arsenal, and then promptly showed no stomach to fight even for a place on the bench.
Chances of vast improvement: Well he’s still there, even if that’s only because Tottenham are unwilling to sell at a stupidly deflated price and nobody is willing to pay more than relative peanuts.

Watford:
Why the disappointment? Having stared at Watford’s squad list on Soccerway and frowned for several minutes (a semi-regular occurrence over the last two years), we asked Twitter’s hivemind. Gavin Cleaver picked Etienne Capoue, who ‘has the skill but nothing like the required application’.
Chances of vast improvement: That’s almost exactly the sentiment within Tottenham about Capoue, so it would be a shock if this leopard now traded in those spots for stripes.

West Brom: Salomon Rondon
Why the disappointment? Had we picked this in December, when Rondon had just scored a hat-trick against Swansea and moved on to seven league goals for the season. The next five months brought one more league goal, with Rondon even left on the bench during April.
Chances of vast improvement: Good, actually. In my head Rondon is over 30, but actually still 27 and with the potential to carry last season’s early form through an entire campaign.

West Ham: Jose Fonte
Why the disappointment? There is nothing wrong with overpaying for an ageing player – particularly in the current market – but only if he hits the ground running. Having looked rock solid at Southampton, West Ham suddenly saw the worst of Fonte.
Chances of vast improvement: The positive spin is that Fonte has proven over the last five years that he is a very capable and competent central defender. The negative spin is that he turns 34 in December.

Source: http://www.football365.com/news/on-the-rebound-the-pls-key-players-looking-to-improve