Juventus & AC Milan would have to agree on the deal before Higuain can get his wish of moving to Stamford Bridge but the transfer would be a significant coup for the Blues, who have lacked a ruthless streak in recent weeks.
Higuain excelled under Sarri during his time at Napoli, scoring 38 goals in his final season before making a big money move to rivals Juve.
The Argentina worldwide set a new Serie A goal-scoring record under Sarri at the Stadio San Paolo in the 2015/16 campaign with 36 goals.
Any agreement to bring in Higuain this month will not be easy, however, with Chelsea reluctant to deviate from their policy of offering only one-year contracts to players over the age of 30 or commit to any lucrative obligation to buy him from Juventus at the end of the season.
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He scored 91 goals during his three years at the club before moving to Juventus in 2016 when the Turin club activated his 90 million-euro buyout clause.
Higuain previously spent six years at Real Madrid after starting his career at River Plate in Argentina.
"To date, Milan knows that Higuain had problems but made him understand that if he remains he must play and take responsibility".
"There's no point following rumours and gossip".
"He is here right now. Seeing as he is here, he needs to get down and actually do something for this team".