The 24-year-old appeared committed to manager David Moyes' plans after penning a new contract through to 2016 as recently as November, but in an interview with a Belgian newspaper published on Sunday Fellaini said he was now looking for a way out of Goodison Park.
"I am just starting my fifth season at Everton, this will be one of my last," he told Het Nieuwsblad.
"I have seen everything.
"In January or at the end of the season I will turn to another club or championship."
Fellaini joined Everton in a £15million move from Standard Liege in 2008 and has scored 22 goals in 130 appearances for the Merseyside club.