The 25-year-old Belgian international insists he will not push for a move away from Goodison Park tat the end of the season, but concedes that the opportunity to test himself in the Champions League would be too good to turn down.
That's not to say that Fellaini can't realise that ambition with Everton, as David Moyes's side are still in the race for a top four finish in the Premier League.
However, yesterday's 2-1 defeat against Norwich City at Carrow Road has presented a brief set-back for the Merseysiders.
Chelsea, meanwhile, are currently ranked in third place going into today's clash with reigning champions Manchester City at the Etihad Stadium, and look more likely to secure a return to Europe's elite club competition.
"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."
Chelsea have long been linked with a move for Fellaini, but so far a Stamford Bridge switch has not been forthcoming.
And, if Roman Abramovich wants to bring Everton's leading marksmen to west London in the summer, then he will have to pay a significant fee for his services.
"Everton paid £20million and do not want to sell me for nothing," added the former Standard Liege star.
"If a big club wants me, they will have to pay the price."
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: http://gms.to/writeforgms