The contracts of Gylfi Sigurdsson, Fabian Delph, and Cenk Tosun will not be renewed.
The club have offered a new deal to Andy Lonergan, while extending Asmir's contract.
Jonjoe Kenny has also been offered an extension but is yet to accept.
Kenny spent time on loan at Celtic and is said to want more playing time in the first team.
In January of last year, Tosun and Sigurdsson both signed from Besiktas for a combined price of over 30 million dollars.
A brief spell at Crystal Palace and a return to Besiktas didn't help Turkish forward Tosun's reputation in the league.
After winning two titles with Manchester City, Delph was limited to 11 league appearances in the last year of his career.
The Toffees were in a battle to stay in the league last season and finished 16th and four points clear of the drop.
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