Reports have suggested Barkley, whose future with the club remains unclear, is facing six weeks out due to a hamstring tear picked up in training, but Koeman could not confirm that.
When quizzed about the situation, Koeman said: "He stopped training, I think it was last Monday. It looks like a hamstring injury but we need to do more tests ... to know exactly what the injury is. We need to wait."
Midfielder Barkley, who is entering the last year of his contract, appears destined to leave the club having turned down the offer of a new deal at Goodison Park.
He has been linked with a move to Tottenham, but Koeman said last week there had been no offers for the England international, with the transfer deadline fast approaching.
Now Gylfi Sigurdsson has signed, it is thought Koeman would be happy to cash in, but there is not much chance of that happening while there are doubts over his fitness.