Sarri's position could be under threat following Sunday's 6-0 loss at Manchester City, another of Lampard's former clubs, as the Blues slipped to sixth place in the Premier League.
"My job is here," Lampard told a Derby media conference on Monday.
"We're working very hard and my thoughts are on Ipswich Town on Wednesday, and Brighton on Saturday.
"But they're going up against an incredible team and I had some time at Manchester City as well. I have some feelings for them. The work Pep Guardiola and their incredible squad have done is something special.