The midfielder has struggled with injuries during his time at Goodison Park.
Now aged 25, Besic has been used sparingly so far this season and has made just two appearances in the Premier League, while he was left out of the squad for the victory over Huddersfield Town last weekend as new manager Sam Allardyce took charge of the club for the first time.
Besic has certainly been unfortunate with some serious injuries, including a cruciate ligament problem that saw him miss the majority of last season.
However, he now faces a major battle to get into the Everton side and may be left contemplating whether it is better for him to move elsewhere in order to further his development.
Capable of playing at centre-back but most effective as a defensive midfielder, Besic is composed in possession and is also effective at closing players down.
However, he is currently behind both Idrissa Gueye and Morgan Schneiderlin in the pecking order at Everton, while there is a possibility that Allardyce may look to bring in a new defensive midfielder in the January transfer window as he seeks to put his own stamp on the squad.
Perhaps the best option for Besic at present would be to go out on loan, maybe to another Premier League club, so that he can play regularly and convince Everton that he is a player worth persisting with.
Besic's contract runs until the summer of 2021 but at present it is difficult to envisage him staying at the club until then if his situation persists.