The Belgium midfielder has long been linked with a move to Stamford Bridge and it is not the first time the player has declared he would be interested in such a switch.
Fellaini is happy at Goodison Park but wants to play Champions League football so he will no doubt wait until the end of the season to see where everyone finishes.
"Am I interested in Chelsea? It's normal, right? I've never played in the Champions League," he told reporters.
"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."
Meanwhile Fellaini has also revealed he will not be leaving on the cheap and any club interested in signing him will have to pay big money, possibly over the £20million Everton paid Standard Liege.
"Everton paid £20 million and do not want to sell me for nothing," he continued. "If a big club wants me, they will have to pay the price."