Sarri’s side lost ground on Manchester City and Liverpool over the weekend as Chelsea rescued a late draw against Manchester United at Old Trafford.
Chelsea dominated the game in the first half, but the lack of an in-form striker was a clear issue as Alvaro Morata disappointed again.
The Daily Mail claim Chelsea are prepared to sign a top-class striker in the winter transfer window, with Krzysztof Piatek and Mauro Icardi top of Sarri’s wishlist.
Icardi would be Sarri’s first choice, but Chelsea understand it will be a huge task to convince Inter to part with their captain mid-season.
Inter would also demand a huge transfer fee, and could cost Chelsea over £90million.
A 1-1 draw with Juventus at the weekend was the first time Piatek had drawn a blank in a game for Genoa this campaign.
The 23-year-old is being tracked by a host of top clubs including Bayern Munich after nine goals in eight league appearances. Genoa signed Piatek last summer for just £3.5m, but are set to make a significant profit on the frontman should they decide to cash in.
Napoli are prepared to pay £30m for Piatek, while reports from Italy suggest Genoa will slap a £40m asking price on their star man.