But I am not anxious because I like to work with players who like to play.
Whichever player Koeman chooses to chase in the summer will give a strong indication of the style of play he wants to implement at Everton next term.
When then asked if he felt confident that Barkley would stay, Koeman said: "No, because it is a long time that he is thinking about his future".
Yet both Barkley and his agent are mindful of the need to be playing at the highest level if he is to make the World Cup squad for next summer.
Asked whether he knew of Barkley's intentions, Koeman said in his press conference: "I don't know".More news: Sino-US deal eases access to markets
The 23-year-old has been offered a new long-term contract at Goodison Park, with his current one due to expire in 2018, but has so far declined to put pen-to-paper.
The 24-year-old was the Premier League's top scorer before Harry Kane overtook him with his four-goal haul against Leicester City on Thursday evening, and Koeman acknowledged that he needs to look at sharing the goalscoring mantle more evenly next season. "I don't need to explain more because if we don't want the player to stay longer, then we don't offer him a new contract".
He continued: "It's after the game or Monday".
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. I expect an answer soon after the weekend and not another ten days'.
"If we can do our business this summer the team for next season will be really strong but it's hard sometimes. I have a good record against Arsenal, let's hope we keep that".