The England international has been impressive since breaking onto the scene with Spurs last season.
Dier, 22, cemented his place in both Tottenham and England’s starting XI last campaign.
However, he has failed to make a mark this season despite Spurs’ solid start.
And according to the Times, Dier is unhappy with his amount of game time he has been given by Mauricio Pochettino.
“Chelsea and Bayern Munich are monitoring Eric Dier’s situation at Tottenham”
He may consider his options next summer if his situation doesn’t improve – but he’s unlikely to force a move in January.
The midfielder is concerned it will hinder his prospects under new Three Lions boss Gareth Southgate.
Dier started Tottenham’s first six games but lost his place after picking up a muscle injury.
He was an unused substitute for their trip to Old Trafford on Sunday with Pochettino opting to play Victor Wanyama and Mousa Dembele in midfield instead.
And Dier’s situation is attracting interest from numerous clubs.
The Times say both Chelsea and Bayern are eyeing the Spurs ace.
Antonio Conte is keen to bolster his midfield at Stamford Bridge with versatile players who can also play in his back three.
And German giants Bayern – who had an approach for Dier rejected last summer – could move for the midfielder again.
Tottenham would reportedly be reluctant to sell Dier, who they paid £4m for in 2014.