The Belgian also spoke of his love for the Toffees though, saying he is happy at the club he has spent five years with, in spite of whatever future decision he may make.
The 25-year-old is the subject of much speculation as he has been in scintillating form this season, leading the club's goalscoring charts with 10 league goals in 21 games.
Fellaini cited his desire to play in the Champions League as a major reason for a potential move, though he emphasised that it had nothing to do with his current employers.
"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."
Having been signed by Everton for a substantial amount, however, Fellaini was adamant that Chelsea, or whoever else may come in for him, should pay a similarly hefty fee.
"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."