Barkley, 23, has one year left on his contract but has failed to sign a new deal. "We made a good offer of a contract, he declined," said Koeman on Wednesday.
Koeman also said he is still interested in Swansea City midfielder Gylfi Sigurdsson after the Welsh club rejected a £40m bid from the Toffees.
The Swans want £50m for the 27-year-old, who scored nine goals last season.
Meanwhile, Everton want around £50m for Barkley but that figure could fall before the transfer window closes on 31 August as he would be a free agent in 12 months' time. The academy graduate has played 150 times for Everton in the Premier League, scoring 21 times, since making his debut six years ago.
"Ross told me at the end of the season he wanted another challenge," added Koeman before Everton's Europa League third qualifying round first leg tie with Slovakia's Ruzomberok at Goodison Park on Thursday (20:05 BST). "His personal situation is really not so difficult. 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.
"Everyone knows what the situation is and that's enough, I don't talk any more about this."