The 36-year-old believes it would be unfair to compare his own qualities with those of the former Arsenal captain but says he hopes Chelsea go from strength to strength
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."