“There is time for him to decide,” the Dutchman said before the Toffees’ 1-0 victory over Watford on May 12.
“The board has been working a long time to sign Ross, to keep him for a longer period but it is up to the player.
“But we will not wait until August. We need to know. Either he accepts the contract or we sell the player. But if you need so much time then you have doubts [about whether he wants to remain].”
We’re now at the end of July and the boyhood Evertonian, who only has one year left to run on his current deal, has still not put pen to paper on fresh terms. His time at Goodison is over.
Koeman confirmed as much last week. Asked if he was making plans for life without Barkley, the Dutchman replied: “Yes, 100 per cent. I knew this already from the end of last season.
“We made a really good offer to him to sign a new contract, he declined that contract and told me that he is looking for a new challenge.
“OK, he is not in Everton’s future any more. It is his decision. I need to respect that and see what happens. He had his groin surgery last week and it will take three or four weeks to be back. His personal situation is not so difficult.”
Even in the current climate, where bumper television deals have considerably increased the wealth of every Premier League club, that is an awful lot of money.
Tottenham Hotspur had appeared to lead the race for the 23-year-old. However, Spurs are believed to be stalling over the midfielder’s £150,000-per-week salary demands. But, over the weekend, reports emerged that Chelsea have entered the race for the England international.
A fee of £50million would make Barkley the second-most expensive signing in Chelsea’s history – on a par with Fernando Torres – behind only summer addition Álvaro Morata.
There is also the question of whether or not he is worth such a fee in the first place.
Everton, of course, are looking after their own interests and may well actually accept a lower price when it comes down to it, particularly as the alternative could be losing Barkley for nothing in just over 12 months’ time.
There is also a good chance that, by unofficially quoting such a sum, Everton are simply hoping to force Barkley’s hand in an attempt to make him sign the extension that has been on the table for a number of months now.
Ever since he made the breakthrough into the Toffees first team at the start of the 2011/12 campaign, Barkley has caught the eye.
His combination of power and technique means he can pose a threat to any Premier League opponent on his day, and he has turned in a number of superb performances in the last few years.
In terms of his output, Barkley’s best season was 2015/16, when Everton struggled under Roberto Martínez. Playing almost exclusively as a No.10, Barkley scored eight goals and provided eight assists.
He bettered that number of assists during the previous campaign (9) but his goal tally fell to six in all competitions.
There has always been a question of whether Barkley can do more: his talent is clear, but he has not yet taken the decisive next step in his career. On one level, perhaps that is a little unfair.
He played in several different roles in 2016/17 and was even dropped for a period by Koeman, but Barkley still played more key passes than anyone in the league but Christian Eriksen, Eden Hazard, Mesut Özil and Kevin De Bruyne.
His tally of 2.3 key passes per 90 minutes is certainly impressive, as is a return of 2.6 chances created per 90.
The biggest question mark surrounding Barkley relates to his decision-making, which can be difficult to pick up in the statistics but will nevertheless be a point of discussion for any interested parties this summer.
There are times when the Everton No.8 selects the wrong pass or makes the wrong choice in possession, and that drawback has not yet been ironed out in the manner many expected it to be when he first broke into the senior side.
At the title-challenging, Champions League level of the game, it is the type of thing that can prove costly, no matter how gifted the player in question is.
It is for that reason that £50million is an unrealistic price for Barkley, and why Chelsea, Spurs or any other club will be wary about spending such a large sum on a player who remains something of a rough diamond.
When splashing that amount of cash on a single footballer, they need to be as complete as possible. Barkley, now 23, still has a way to go before he can be considered that.