Lampard left Stamford Bridge this summer after a trophy-laden 13-year spell which saw him win 11 major honours and establish himself as one of the greatest players in the club's history.
Jose Mourinho recruited former Arsenal captain Fabregas in a £30 million deal from Barcelona to help fill the void left by the departed Lampard, and the 36-year-old is hoping the Spaniard shines in a Blue shirt.
"I’d hate to put too much pressure on Cesc - we’re all individuals," he told reporters at his unveiling as New York City FC's latest signing in a press conference in Brooklyn. "He has his qualities and I have mine.
"It’s a new chapter in a lot of ways at Chelsea and I wish them every success. We know Cesc is a world-class player. We’ve had our battles in the past but I wish him all the best because I wish Chelsea all the best."
Lampard also revealed he has yet to decide on whether to retire from England duty following his move to the MLS, but hinted that a firm announcement will be made soon.
"In terms of England, my main priority was getting my personal future sorted out," he added.
"Now I have to think about England and make a decision. Now I know where I’m playing my football it won’t be long."