Lampard is set to leave the Stamford Bridge club at the end of the season after Chelsea reportedly made it clear that they would not be offering the England international a new contract. His present deal expires at the end of the season, and while Lampard would like to extend his contract, the club expects him to depart on a free transfer this summer.
And Rafa Benitez is prepared to trigger the £22m buyout clause in Fellaini's contract this summer as the Blues look to replace Lampard. Fellaini would not be a direct replacement for the Chelsea legend, but his versatility, height and power are valued by the Stamford Bridge heirarchy.
The Times reports that Fellaini signed a five-year deal in 2011, which inserted a £22m minimum fee release clause that can only be triggered by a bid from a Champions League club.
The European champions crashed out of the Champions League at the group stage this season, but are well-placed to secure qualification for next year's competition.
The Blues recently activated Demba Ba's release clause, signing the former-Newcastle striker for a fee in the region of £7.5m, and they are believed to be ready to use similar tactics to bring Fellaini to Stamford Bridge.
The Belgium international moved to Goodison Park for £15m in 2008, and has flourished under the guidance of David Moyes.
His performances this season in a more advanced role have been superb, and the midfielder is one of his club's top scorers, although he can also operate as a defensive midfielder or as an out-and-out striker.