The 34-year-old has been at Stamford Bridge since 2001 but, as he enters the final year of his deal, some have suggested that he could be phased out and eventually released despite the player's desire to stay on.
"I am, yes," Di Matteo told the press when asked if he was hopeful that any talks to renew Lampard's contract would be successful, though he added that “these are talks between the club and the player".
"I've been very happy with Frank and he shows the qualities that he has in every game that he plays, so [he's] a very influential player within the group as well."
The England star, who captained his country against Italy on Wednesday, looks likely to be the subject of similar gossip to Didier Drogba, who eventually decided not to renew his Chelsea contract at the end of last season, but the Italian is not expecting the same level of scrutiny this time around.
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"I don't think I'll be answering this question all the time," he opined.
"I think that's between the player and the club to sort out and when that's going to be, when the time is going to be.
"He's in good shape, he's not suffered any major injuries and he looks after himself. We've seen that many players who live a professional life can go on and play up to their late 30s."
With his age advancing, Lampard is expected to drop into a deeper midfield role than that to which he has previously been accustomed, and Matteo gave credence to that possibility.
"I don't think we're going to change exactly everything there is about Frank and take his qualities away," stated the Blues boss. "We want to enhance his qualities within the team.
"He certainly has a little bit of a different role but we're still wanting to do what is best for him, trying to go forward and he's got good timing or arrival in the box and scores goals for us as well.
"We have a lot of competition in midfield - that is very good - but we have a lot of games as well and competitions that we're going to be playing in," Di Matteo continued.
"So there will be time for everybody and that's the situation for all the players.
"He's an important player, Ramires is an important player, [Juan] Mata's an important, [John Obi] Mikel's an important player, [Michael] Essien ... We can't think that we can only count on 11 players or 10 players."