The Premier League champions suffered their ninth defeat of the season last night in the League Cup away at Stoke and are slumped down the table in 15th.
Lampard, who won two Premier League titles under Mourinho, says he is still the right man for the job and that his record speaks for itself.
“For sure. His record speaks for itself,” Lampard told ITV News. “I know he’s the most successful manager in Chelsea’s history.
“I’m sure he’s tearing his hair out and wanting to turn the corner. I’m sure the players are wanting to perform.
“I know the quality in the dressing room. I know the squad. I know people like John Terry with the desire to keep Chelsea up where they always are.
“That will turn around very quickly and hopefully they move on and be where we expect them to be.”
The English midfielder scored three goals in 10 MLS appearances in his debut season.