The 25-year-old Belgian international has been in scintillating form, and has already netted six Premier League goals for David Moyes' side this season, prompting a raft of speculation linking him with a move away from Goodison Park.
Blues boss Roberto Di Matteo has been linked with a January bid for Fellaini, as he looks to add even more attacking options at Stamford Bridge in the upcoming transfer window.
The Everton star is under contract on Merseyside until 2016, but with talk of a big-money move doing the rounds, Fellaini has been forced to concede his intentions of gracing the very highest level, and ambition of playing in the Champions League.
"There is interest in me," he is quoted as saying by ESPN. "But Everton are an ambitious club as well.
"I don't think they will let their best players go just like that. I want to play for one of the biggest clubs one day. But I am patient."
If Fellaini were to join Chelsea, he would join a growing contingent of Belgian's in west London, with summer signing Eden Hazard the stand-out arrival to make his mark. Romelu Lukaku, Thibaut Courtois and Kevin De Bruyne are also on the club's books, but continue to gain experience on loan away from Stamford Bridge.