The Belgian international has been strongly linked with a move to Stamford Bridge for the past 12 months and the European champions were reported to be considering a bid in January - but that never materialised.
Now Fellaini appears to be growing frustrated - whilst maintaining he is happy at Everton, where he has three years remaining on his contract - he has told Chelsea to step up and make a bid if they indeed want him.
"If Chelsea want to sign me, then they need to come forward with a bid for me," he is quoted by the Sun.
"I have heard about Chelsea's interest but I've honestly not spoken to them.
"Every season I've been here, top clubs have been asking about me but, for now, I'm happy at Everton."
Fellaini insists that getting Everton into the top four would mean everything to him.
He added: "It might feel better to play Champions League football for Everton than Chelsea, as they gave me my debut in England."
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