If the Blues sign Higuain or Wilson, then current forward Alvaro Morata is expected to move back to Spain with Sevilla heavily interested in signing him.
"Chelsea have an agreement with Higuain to take him immediately", Gazzetta reported.
The Argentina global set a new Serie A goal-scoring record under Sarri at the Stadio San Paolo in the 2015/16 campaign with 36 goals.
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.
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However, Milan sporting director Leonardo warned on Tuesday he had to get down to work.
When asked about Chelsea's interest in Higuain, Leonardo said: "There's no point following rumours and gossip".
"We want to continue to take the club forward and the team forward, and to do that, we've got to keep our best player".
Chelsea, for their part, are in need of a striker after deploying Eden Hazard as a false nine for a large chunk of the season.
The 26-yer-old Spaniard has struggled for form since his £65m arrival at Stamford Bridge from Real Madrid in 2017.