The Blues suffered their ninth league defeat of the 2019-20 campaign at home to Manchester United on Monday night, meaning that there are now just three points between fourth-placed Chelsea and Ole Gunnar Solskjaer's side in seventh.
According to The Telegraph, Lampard's position at the club will 'come under greater scrutiny' if the club's former midfielder is unable to secure a top-four finish this term.
The report also claims that the manager's decision not to recall Kepa Arrizabalaga for the clash with United has led to surprise within the club.
The world's most expensive goalkeeper was dropped against Leicester City before the winter break and was again on the bench against the 20-time English champions on Monday.
Lampard's management of the squad is allegedly also being questioned, suggesting that the 41-year-old's future at Stamford Bridge is far from secure despite only taking over last summer.
Chelsea are next in league action at home to Jose Mourinho's Tottenham Hotspur this weekend.