The Belgium international has been heavily linked with a move away from Merseyside in recent months, with the 25-year-old revealing an ambition to play in the Champions League.
Fellaini remains under contract at Everton until 2016, but after signing a new five-year deal in 2011, had a £23million buy-out clause written into his current deal.
The Toffees will be powerless to prevent him from leaving if that valuation is met by a club that has qualified for Europe's elite club competition.
However, the Blues will face serious competition for the player's signature, with Russia rivals Anzhi Makhachkala and Zenit St Petersburg both also monitoring his situation.
If Everton fail to finish fourth in the Premier League this year, which now looks increasingly likely after Saturday's 1-0 defeat to Sunderland left David Moyes's four points behind Chelsea - who have two games in hand - then they will have almost no chance of retaining Fellaini's services for 2013/14.