Boss Koeman is playing it cool despite the £70m-rated star’s refusal to sign a new deal.
Lukaku, 23, also publicly criticised the club this week for failing to sign top players and claims the club lack ambition.
But Koeman will still pick 19-goal Lukaku for their home game with Hull, and claims he is relaxed about the Belgium hitman as his current contract runs for two more years.
“Every player has ambition, everyone wants to play in the Champions League”
Everton boss Ronald Koeman
Koeman said: “Every player has ambition, everyone wants to play Tuesday or Wednesday in the Champions League, that’s a normal ambition.
“If there’s one club outside the big six to take the next step, it’s us.
“Everyone sees now the difference between this season and last. But it’s impossible to do this in one transfer window, in one season. It takes time.
“I spoke with Rom about this project in the summer, and during the season we have had several talks.
“I am not afraid of his situation because he has two more years on his contract. Of course that gives me confidence.
“Everyone knows what can happen in football – but you need to respect your contract.”
Chelsea are ready to step in with a £70m bid to take Lukaku back – and are also eyeing Ross Barkley.
The England midfielder, 23, is approaching the last year of his contract and Koeman is clear that without a new deal he will be sold.
Koeman said: “Normally you make decisions at the end of the season – you need to sign a new contract or you sell the player.
“There is no ultimatum, it’s business. I spoke to Ross and it is up to the board to get the contract over the line.”