Koeman says the Toffees are looking for players who operate in Barkley's position irrespective of whether or not the 23-year-old midfielder signs a new deal, with his current contract expiring in the summer of 2018.
The board has been working to try to get Barkley re-signed, and the England international was told last week by Koeman that he had until the end of this season to make a decision on his future, with the Dutchman saying at the time: "Either he accepts the contract or we sell the player."
Everton's season concludes with Sunday's Premier League trip to London to face Arsenal and asked on Friday whether there was any update on Barkley's future, Koeman said: "I don't know. It is after the game, on Monday - then we will know it."
When then asked if he felt confident that Barkley would stay with Everton, Koeman said: “No, because it is a long time that he is thinking about his future.
“But, okay. I'm not worried, because I like to work with players who like to stay.
“And - it is not about his decision - we will go on. We are looking for players in that position.
“Even if he stays, there will be more competition for him next season.”
Koeman stressed Everton do want academy graduate Barkley to stay, and admitted he does not know what will happen if there is no change to the current situation come Monday.
“If you offer a player a new contract, and a good contract, that means that you like to keep the player,” he said.
“I spoke to the player, the board spoke to the player and his agent. We need an answer after the weekend.
“We will see what the answer will be - and I don't know what will happen if he doesn't give any answer about that.”
