It is understood the Belgian midfielder can leave Merseyside for £22 million for a club qualified for the Champions League - or £24m for teams outside the top four.
Fellaini has been linked with Chelsea in the past year, and more recently Manchester United when David Moyes - the man who brought him to England - announced he was taking over from Sir Alex Ferguson.
Speaking to the The Times, Everton chairman Bill Kenwright said: "Fellaini insisted on [the clause]. I have to say he has given me every indication he doesn't want to go."
Arsenal have already made moves for Queens Park Rangers and Brazil goalkeeper Julio Cesar and have been linked with Swansea defender Ashley Williams.
But according to Goal.com, Arsene Wenger will be handed a £100 million warchest in the transfer window and Fellaini is the Frenchman's No. 1 target.
Meanwhile, there is speculation that Everton defender Leighton Baines, whose contract has two years to run, could link up with Moyes at United.
Asked whether the England full-back will be offered a new deal, Kenwright added: "Absolutely right. That's started; started in that he knows we want him to stay."
