The 24-year-old playmaker only joined the Toffees in the summer from Europa league finalists Ajax, as he captained the Dutch outfit to within an inch of European glory under now Borussia Dortmund manager Peter Bosz.
Making 50 appearances in all competitions last season, the 16-time Netherlands international amassed an impressive 20 goals as well as adding 12 assists for Ajax - which saw Everton wield their spending power.
Owner Farhad Moshiri splashed out £25million on Klaassen, but fast forward until now and it simply has not clicked for the attacking midfielder. No goals and just one assist is a fraction of the form he produced last season - coinciding with Everton's abysmal run of defeats.
Now, Fenerbahce believe they can take advantage of the midfielder's struggle to cope with English football by luring him to Turkey, but the report claims Everton will not let them do it on the cheap.
It is believed that Fener want a loan move until the end of the season, with Everton charging 2.5million Euros (£2.2million) to let the Dutchman leave on a temporary basis.
Klaassen has a contract at Goodison Park until the summer of 2022 and the Toffees will be desperate to see him reignite his best form, much like Oumar Niasse has done at Hull before returning to Everton to shine in front of goal.