Owner Roman Abramovich is ready to splash around £20 million for the Belgium international who will come in as a replacement for veteran Frank Lampard.
Fellaini, 25, who has been playing in a more attacking role this season, has attracted top clubs after a run of eight goals in 16 appearances for Everton.
But the Everton star is edging closer towards the exit door after being handed a three-match ban for a headbutt on Stoke City captain and defender Ryan Shawcross. Toffees manager David Moyes is furious about the incident involving Fellaini and the club is set to punish him with a heavy fine of £150,000.
However, Chelsea will not back down despite all these incidents as they look to strengthen their midfield.
Lampard, 34, has been linked to several clubs across Europe and Chelsea boss Rafa Benitez recently revealed that he could leave the club at the end of the season.
Meanwhile, Ramirez is the only player to play in the middle while Benitez used defender David Luiz during their Club World Cup campaign. Oriol Romeu is out injured and John Obi Mikel will be on national duty at the African Cup of Nations.