But the prospect of Champions League football at Stamford Bridge would be hugely tempting if they finally make a firm offer.
And the 25-year-old admitted in the People: "Am I interested in Chelsea? It's normal, right? I've never played in the Champions League!
"I'm happy here, I know everyone, I get along with my team-mates. It's my home. On the other hand, I also want to take the next step. Fate will decide.
"Everton paid £20million and do not want to sell me for nothing.
"If a big club wants me, they will have to pay the price."
Is Fellaini the right signing for Chelsea. Are the Blues the right move for the big man? Give us your shout below...