Club chiefs are already looking at alternatives to Lampard if they were to sack the 42-year-old.
Chelsea have now lost four of their last six Premier League matches and sit eighth in the table.
There is respite from league action next week as they face Morecambe next week in the third round of the FA Cup.
Following the defeat to City, Lampard admitted he was feeling the heat for his position.
“I always feel heat, I even did when we were on our good run,” Lampard said.