Jagielka has been at the club for almost 10 years after joining from Sheffield United back in July 2007, but his days may be numbered at Goodison Park.
The club captain has struggled to be a regular starter in recent weeks, as Koeman has preferred Ashley Williams and Ramiro Funes Mori at the heart of his defence, meaning that the 40-cap England international has been forced to sit on the bench.
Asked whether Jagielka may leave, Koeman said: "I don't know, it's all about if there is interest for Jag. Of course the last few weeks he did not start. He is important, he is the captain of the team.
"He is not happy because he is not starting and that's a good signal. What you need to do as a player is fight and make it difficult for the manager".
Meanwhile, Deulofeu has been told he is free to leave, albeit on a temporary basis. The ex-Barcelona youngster was expected to join AC Milan on loan, but a deal has allegedly stalled as the Italian club are not willing to pay a loan fee for the player.