Phil Jagielka could be set to leave Everton in the January transfer window
The club captain has been heavily linked with Sunderland where he would hook up with his old boss David Moyes after finding his first team opportunities limited.
"He is not happy because he is not starting and that's a good signal," said Koeman. "What you need to do as a player is fight and make it difficult for the manager.
Ronald Koeman insists Jagielka is unhappy due to his lack of starts
"I don't know [if he will leave this month], it's all about if there is interest for Jag. Of course the last few weeks he did not start but he is important – he is the captain of the team."
Jagielka has slipped behind Ashley Williams and Ramiro Funes Mori in the pecking order for the heart of the Everton defence. Moreover, Koeman is also understood to be keen to reinforce his defensive options further before the window shuts.
Gerard Deulofeu, who has found his time on the field even more limited than Jagielka, looks set to leave the club on loan with Middlesbrough the most likely destination despite interest from AC Milan.
Gerard Deulofeu also looks set to leave Everton this month
Koeman said: "It's a difficult situation for the player. If he finds a solution to go and to play and to get game-time then it's not a problem.
"You have to always look for first what's the best for the club and second what is the best for the player, and for Gerry the best [solution] is that he gets game-time somewhere."
The Everton manager also confirmed that the club have finally pulled the plug on a move for Standard Liege striker Ishak Belfodil despite a £10million deal coming close to being agreed last week.
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Koeman said: "He was one of the players on the list but we took the final decision to not sign the player."