Asked directly by reporters on Friday if he was confident about Barkley's contract situation, Koeman said: "No".
Whilst Koeman is clearly keen for the 23-year-old to stay put at Goodison Park, he will not be held to ransom and has lined up targets to replace him.
'I have got a picture of where we need to improve.
Everton manager Ronald Koeman admits that he is not confident about the prospect of Ross Barkley signing a new contract at the club.
"I spoke to the player, the board spoke to his agent".
"We had several meetings and we know what we want".
"We need an answer after the weekend, I don't know what will happen if he doesn't give any answer".More news: James Wan shares picture of Amber Heard in new 'Mera' costume
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"It is after the game, on Monday - then we will know it".
And it could be Barkley's final game for the club.
Koeman's men face a trip to Arsenal on Sunday to complete their Premier League campaign and, with Barkley yet to sign the deal offered by Everton, the Dutchman signalled that the midfielder could now leave.
Merson said of the England global, "I'm a big fan of his and have a lot of time for him, definitely, but if he goes to Tottenham he won't play in that team".
Harry Kane's four-goal haul at Leicester City on Thursday sent the Tottenham striker two goals ahead of Everton's Romelu Lukaku in the race for the Premier League's Golden Boot award.
Lukaku, now on a deal that has just over two years left, has scored 24 league goals this season, which did have him in pole position for the golden boot until Tottenham's Harry Kane netted four times at Leicester on Thursday to take his tally to 26. Either he accepts the contract or we sell the player.