Lampard has been adamant the Blues – who had their transfer ban lifted ahead of the January window – would only bring players in if the deals were right for the club.
However, after Sunday's (AEDT) 1-0 defeat at Newcastle United, Lampard acknowledged Chelsea need reinforcements in the final third and will be looking to do business if possible this month.
Cavani wants to leave PSG after falling behind Mauro Icardi in Thomas Tuchel's pecking order, though a bid from Atletico Madrid has been rejected.
Lampard has spoken of his admiration for Cavani, but stressed he is not close to adding to his squad.
"He's a great player, I played against him and I always loved his mentality and his attitude and obviously his goalscoring record speaks for itself," Lampard said of Cavani during a press conference on Monday.
"Not absolutely aware what his situation is, so we'll see. He's an experienced player but so are many other players out there.
"We are young as a squad, we know about the transition, so bringing in experience is something I'm not shying away from because I think younger players sometimes need help and if that's the case then that may help us.
"I think long term in January is difficult. We haven't seen many. I think it's difficult so short term is certainly something we'd look at because I think there are issues which are pressing for this season to finish where we want.
"We're looking, but nothing to tell you that might happen right away."
Lampard maintained Chelsea will not rush into any deals, while adding there was no further news on the potential departures of Olivier Giroud and Victor Moses.
"I don't think it hastens it, it's just a case of us not doing any business in the previous window so it's something we've seen there's a bit of a problem [scoring goals]," he said.
"There's two things to do, work hard with the group here and then from a club point of view and my point of view, if we can improve in areas in terms of goalscoring it's something we for sure have to look at."