The Belgium international has been in sparkling form this season, fuelling speculation that he could be the next high-profile figure to head through the exits at Goodison Park.
Talk of a big-money move during the January transfer window is currently doing the rounds, with Chelsea among those said to be keen.
Fellaini, who is under contract at Everton until 2016, concedes that he has ambitions of gracing the very highest level, but he will not be pushing for a move and, at the age of 25, appreciates that time is on his side.
"There is in 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."