The 23-year-old has been offered a new deal by the Toffees but has stalled on committing his future to the club amid reported interest from Tottenham Hotspur.
Koeman has given the England international a deadline of the end of this week to decide whether or not he wants to stay at the club, but the manager is unsure where Barkley's future lies.
"It is after the game, on Monday – then we will know it," Koeman told reporters regarding Barkley's situation.
"No [I am not confident], because it is a long time that he is thinking about it. But I'm not worried, because I like to work with players who like to play."
Barkley has made 35 Premier League appearances for Everton this season, scoring five goals.