The England international has rejected the offer of a new contract at Goodison Park and is now into the final 12 months of his existing deal.
Koeman has previously suggested that he will attempt to cash in on the midfielder, with Tottenham Hotspur and Chelsea both said to have shown an interest, but no official bids have yet been made.
Reports in the British press on Wednesday morning suggested that Barkley is facing a further six weeks on the sidelines due to a hamstring injury, though Koeman is unsure of the severity of the problem at this stage.
"He stopped training last Monday. It looks like a hamstring injury but he need to do more tests today and tomorrow to know exactly what the injury is," he told reporters.
Asked about the Englishman's future on Merseyside, Koeman added: "There is no update about his situation. I will wait until the end of August."
Barkley, reportedly valued at £50m by Everton, played a part in 13 Premier League goals last season.