Following a recent run of form, which included a 4-0 thrashing at Bournemouth followed by a 6-0 demolition against Manchester City on Sunday, there are rumours that Sarri could lose his job just seven months after taking over at Stamford Bridge.
As a former Chelsea legend who moved into management last summer, Lampard will inevitably be linked with the post whenever it becomes available, but he insists he is focused on the job in hand at Pride Park.
"My job is here," Lampard told a Derby press conference on Monday, quoted by the Evening Standard. "Were working very hard and my thoughts are on Ipswich Town on Wednesday, and Brighton on Saturday."
Chelseas defeat against Manchester City was their heaviest in any competition since a 7-0 loss to Nottingham Forest in 1991, but Lampard believes his former team will bounce back.
"With my Chelsea hat on, 13 years as a player there, you have a feeling for it and its not nice, its not easy. It doesnt happen to Chelsea much so when it does its a shock," he said.
"For Chelsea it was a tough day. With all top teams the important thing is you come back strong, no matter what type of defeat. What makes top teams is resilience and Chelsea as a club will have it."
Under Lampards guidance, Derby are strong contenders for promotion this season, with only goal difference separating them from the play-off places at present.
They are also through to the FA Cup fifth round, where they face Brighton on Saturday.