The 27-year-old former Arsenal captain signed from Barcelona in June after Chelsea's record goalscorer Lampard left the club at the end of last season.
Fabregas scored a superb individual goal in Chelsea's 2-1 win over Ferencvaros in Budapest on Sunday, on a day when Lampard was sitting in the stands for Manchester City after signing on loan from New York City FC.
The win in Hungary was Chelsea’s final pre-season friendly before next Monday's Premier League opening contest at Burnley.
Mourinho told the club official website: "Frank is the history of the club, history nobody can forget.
"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."
The league starts on Saturday, but Chelsea are not in action until they visit promoted Burnley on Monday - a fixture for which Mourinho is confident his team will be perfectly prepared.
"It's been a difficult pre-season because we started with seven players," said Mourinho. "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."