The local-born England international, who joined the Toffees academy as an 11-year-old, had been stalling on a new £100,000-a-week contract offer made earlier this year and Koeman gave him a deadline for the end of the season to sign it or be sold.
Barkley, who has less than a year remaining on his current deal, has subsequently told Koeman he wants to move to another club and the manager’s response was predictably blunt.
Asked whether Barkley would leave, the Dutchman said: “Yes, 100%.
“We made a good offer to him to sign a new contract, he declined that contract and told me that he is looking for a new challenge.
“It is not (an) Everton future any more, it is his decision, I need to respect that and then we will see what happens.
“My priority is not Ross, with respect, it is his decision. I look more to other players. I knew (this) at the end of the season.”
Tottenham were linked with a move for Barkley, although their interest appears to have cooled after reports he wanted £150,000-a-week, with speculation also claiming Manchester United and Arsenal have considered the midfielder.
However, at the moment his options look limited after Koeman said there were not any realistic offers on the table and he was prepared to allow Barkley to run down his contract if necessary.
That presents the midfielder with a potential prospect of not having any game time in a season leading up to a World Cup.
“What I heard from the board is there is not really an offer on the table for Ross,” added Koeman.
Barkley is currently injured, having had surgery on a minor groin problem, and will be out for possibly the next month. However, he will be expected to return to training as normal when he has recovered and Koeman has no plans to isolate him.
“He had his groin surgery last week and normally it takes three to four weeks before he is back,” he added.
“He has one more year of contract and we work with respect for people and if he is back after his surgery, after the injury, and back for training he will be part of first team sessions.”
Asked whether he had noticed a change in the player since his return for pre-season Koeman said: “No, he is the same.”
Koeman has signed six players already this summer and will continue to plough ahead with a move for Swansea’s Gylfi Sigurdsson, viewed as Barkley’s replacement, after having a second bid of £45m turned down.
Injury to centre-back Ramiro Funes Mori also means he is looking for defensive reinforcements plus another striker.
“We lost Funes Mori with a knee injury so we are looking to replace him,” said the manager. We lost (Romelu) Lukaku so we brought in Sandro Ramirez and we will try to get another striker in and maybe one more.”
News of Barkley’s impending departure overshadowed Wayne Rooney’s return to Goodison Park with the former Manchester United forward set to start against Slovakians MFK Ruzomberok in tonight’s Europa League third-round qualifier.
The 31-year-old has made an emotional return to his boyhood club 13 years after leaving and has already had a positive effect within the squad.
“We know he is used to winning titles, which is what we want at Everton,” said Koeman.
“The confidence in his football is what I like but what I really like is his ambition in training, showing to the young lads his experience and explaining things. He is a big player in England and of course young players know everything about Wayne Rooney and he is an example about winning titles and he can be a teacher for young players off the pitch.”