19 May, 2017
Tottenham are among a number of clubs understood to be interested in the 23-year-old with manager Koeman last week telling him to sign a new deal before the end of the season or he will be sold this summer.
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 global Kane.
Koeman said he anticipates a decision on Barkley's future by Monday at the latest.
"The board has been working a long time to sign Ross for him to stay for a longer period but it is up to the player".
'I spoke to the player. I don't know if he won't give an answer.
'We have had several meetings. "It is up to the player and he needs to make a decision". If we can do our business this summer, the team will be really strong for the next season. I can deal with that. "Certainly for Everton they need a bit more freshness in their team and maybe Ross [Barkley] does, in terms of getting a new club, having to earn a place in a team and not have the comforts of being at home and living in his hometown". Let's hope we can do good business. Barkley is certainly going to move to a big club but I don't think it will be Manchester City. I have got the picture but the picture is not for you.
"If you offer a player a new contract, a good contract, that means that you like to keep the player", he said at a press conference ahead of Sunday's final Premier League fixture at Arsenal.