Koeman not confident Barkley will sign new Everton deal
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.
Asked directly by reporters on Friday if he was confident about Barkley's contract situation, Koeman said: "No. I spoke to the player, the board spoke to his agent. I don't know if he won't give an answer. I don't know.
"We will go on and we're looking for players in that position. If he stays there will be more competition.
"I am not worried because I like to work with players who like to play.
"If you offer a player a new contract, and a good contract, that means you want to keep the player."
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.
And Koeman accepts it will now be tough for Lukaku - who like Barkley has been linked with a move away from Goodison Park - to overhaul England international Kane.
"Expect a hat-trick against Arsenal away? It will be difficult but we will try to help," Koeman said. "We didn't expect four goals from Kane.
"Even if he doesn't win the Golden Boot, 24 is a good number of goals. He knows he can improve in several aspects, to keep the ball better, be stronger and do better pressing. But that's what we work on.
"We need to keep his goals and find more players to score more than four or five goals in one season."