"I'm not anxious because I like to work with players who like to stay".
The Dutch manager had also informed Barkley he had until the end of the season to make his choice, or he would be sold regardless, but with two days to go until Everton's final match of the campaign the England worldwide is still to give his answer.
Asked directly by reporters on Friday if he was confident about Barkley's contract situation, Koeman said: "No".
Asked at a news conference ahead of Sunday's trip to Arsenal whether there was any update on Barkley's future, Koeman said: "I don't know".
"You like to keep your best striker, your top scorer, but we also need around that position more productivity".
The England midfielder has one year remaining on his current deal and is yet to agree on new terms despite being offered an extension by the club.More news: Hunt for Good Samaritan who helped teen 'sex slave' escape in Sydney
He stressed that Everton wanted Barkley, who came through their academy ranks, to stay and added: "If you offer a player a new contract, and a good contract, that means that you like to keep the player". The Dutchman gave the Wavertree-born star until the end of the season to make the club aware of his decision.
Koeman is expecting a decision on his future by Monday, and doesn't know if he will carry on playing for Everton once the season is finished.
Whether they could obtain such a fee is open to debate and it is possible that Barkley's position will not have been finalised before Everton return to pre-season training on July 3; their first Europa League game is scheduled for July 27.
"We had several meetings and we know what we want".
"If we can do our business this summer the team for next season will be really strong but it's hard sometimes. Let's hope we do good business".