The 27-year-old former Arsenal captain signed from Barcelona in June after Chelsea record goalscorer Lampard left under freedom of contract at the end of last season.
Fabregas scored 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 - in the Blues' penultimate pre-season friendly before next Monday's Premier League opening contest at Burnley.
Mourinho said on chelseafc.com: "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."
Chelsea returned from Hungary late on Sunday night ahead of their match with Real Sociedad on Tuesday.
It is still too soon to know the full extent of the ankle injury which forced Didier Drogba off during the first half against Ferencvaros.
Drogba said on chelseafc.com: "I twisted my ankle and I couldn't continue.
"In the next few days we are going to do some treatment and I hope everything will be better."