Fabregas shone in Chelsea's 2-1 friendly victory over Ferencvaros on Sunday and netted the game's winning goal with a well-taken finish after a mazy dribble into the penalty area.
The Spain international agreed a five-year deal at Stamford Bridge in June after three seasons with Barcelona in La Liga, and was immediately identified as a successor to Lampard, who scored a club-record 211 goals in 648 appearances for the club.
Lampard was released by Chelsea at the end of last season and will spend time on loan with Premier League champions Manchester City ahead of a move to new MLS franchise New York City
"Frank is the history of the club, history nobody can forget," Mourinho told Chelsea's official website.
"Fabregas is the future; history is history but the future is more important at the moment.
"My opinion, and the opinion of my players, is that Fabregas is the right player to occupy that central position in midfield."
Chelsea, who open their Premier League campaign against new boys Burnley at Turf Moor next Monday, are one of several clubs who have had to deal with players reporting back for training at different times following their exertions at the World Cup in Brazil.
"It's been a difficult pre-season because we started with seven players," Mourinho added. "After that, step by step, players were arriving after the World Cup and holidays.
"Finally, in this last week we've had everybody together but obviously not everyone is prepared.
"For example, [Branislav] Ivanovic has been training for one month, [Andre] Schurrle has trained for five days, so there is a big difference between players.
"We have to play the first league match next weekend and we will be ready for that."
