Ross Barkley has until the end of this season to decide his Everton future.
The England international is yet to agree a fresh contract extension with the Blues as he prepares to enter the final 12 months of his existing deal.
Ronald Koeman previously warned Barkley that he risks being sold this summer unless he is able to commit his long-term career to Goodison Park.
And the Dutchman believes that the Everton midfielder is increasingly best served in staying with his boyhood club.
He said: “I’m not involved in the negotiations but I know that the board is talking to his agent.
“It’s not about one week but we need to know the answer before the end of the season.
“It’s always about the contract and, okay, we will offer him the contract that is good and normal, what the player is [worth].
“I spoke to Ross several weeks ago and he mentioned his ambition is Champions League.
“But I told him I have the same ambition and I think we are going in a good direction.
“Of course he’s one of the key players; a kid of the club, a kid of the town and, in my opinion, there’s no better place for him to continue his football than Everton.”
Koeman also responded to Barkley being caught up in an attack at a Liverpool city centre bar just hours after Everton’s 4-2 win over Leicester City.
“I think it could have happened to everybody in town,” admitted Koeman.
“Maybe now he realises it’s maybe it’s the wrong time in the wrong place to meet crazy people like that.
“It’s not about experience. You played the game, you won the game, you go out. It’s no problem for me if your behaviour [is good].
“He didn’t drink, he was driving his car, if you meet that [sort of] people, something can happen. Maybe that’s the reason that I live outside of the town.”
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