The Blues have won just one of their last six league matches and were beaten 3-1 at home by Manchester City on Sunday.
Lampard made a number of summer signings in an attempt to bolster his squad, though the likes of Kai Havertz, Timo Werner, and Hakim Ziyech have struggled to settle in west London.
Lampard took over at Stamford Bridge in the summer of 2019 and impressed in his first season with Chelsea under a transfer embargo.
Though a title challenge was expected this season given the summer business and impressive start to the campaign.
Defeat to City puts Chelsea into eighth though, and The Athletic report that the Blues are looking at other options.
It’s claimed that Lampard’s job is under serious threat, though there is no timeframe for when the former Derby boss could be sacked.
But Chelsea owner Roman Abramovich has a view of showing their former midfielder the door should the current slump continue.
The Blues take on Morecambe in the FA Cup next weekend before clashes with Fulham, Leicester and Wolves.
Chelsea have three fewer points after the first 17 matches of this Premier League season (26) than they did at the same stage of the 2019-20 campaign.
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It’s a return that is reportedly regarded as unacceptable given Lampard spent over £200m in the summer, with Ben Chilwell, Edouard Mendy and Thiago Silva also signing.
It’s believed Mauricio Pochettino would have been one of the most attractive candidates, though the former Tottenham boss was appointed as new PSG manager this weekend.
The Athletic add that Chelsea will not hesitate to act sooner rather than later if they decide a change is required.