The defeat at the hands of Leicester on Tuesday night was the fifth loss in eight league matches for the Blues.
Several managers have been linked with Chelsea with Lampard now staring at the axe at Stamford Bridge as Roman Abramovich contemplating the club's next move.
It remains to be seen whether Lampard will make it through to the next match, which is in the FA Cup against Luton Town this Sunday.
Thomas Tuchel, recently sacked from Paris Saint-Germain, is the bookies' favourite to take over.
But Massimiliano Allegri has also been linked with the Italian keen on taking a job in the Premier League after learning English over the past two years.