Higuain, 31, is halfway through a season-long loan at AC Milan from Juventus, with an option to make the deal permanent.
However, Chelsea have reportedly reached an agreement with the Italian sides to bring Higuain on loan with the option to make the deal permanent or extend the loan for another 12 months at the end of the season.
As a result of Higuain’s arrival, Alvaro Morata is set to leave Chelsea to return to Spain at Atletico Madrid on loan.
Higuain scored a record 36 Serie A goals under Sarri at Napoli before moving to Juventus in 2016 for then the third-highest transfer fee of all time in a 90 million euro move ($103 million).
After winning two league titles with the Bianconeri, though, he was forced out by the signing of Cristiano Ronaldo in July.
Milan paid 18 million euros to sign Higuain on loan, with a clause to make the deal permanent for a further 36 million euros.
Yet he has struggled to settle at the San Siro, scoring eight goals in all competitions and was heavily criticised for a meltdown that saw him sent off in a 2-0 defeat to Juventus in November.
Higuain only made a late appearance as a substitute when the sides met again, with Juventus 1-0 victors on Wednesday in the Italian Super Cup, which was held in Jeddah, Saudi Arabia.
Milan boss Gennaro Gattuso insisted Higuain had been suffering from a fever, but admitted earlier this week that the striker was determined to link up once more with Sarri.
“When a player makes up his mind it becomes hard to convince them otherwise,” said Gattuso.
Chelsea are badly in need of a centre-forward, with the form of the misfiring Morata and Olivier Giroud prompting Sarri to use Eden Hazard in an unfamiliar false nine role in recent weeks.
Morata signed for a then club-record £60 million ($77 million) in July 2017 from Real Madrid, but after a bright start has become increasingly bereft of confidence over the past year.
After two spells with Real, Morata is set to switch sides in the Spanish capital by joining Atletico, where he started his career as a youth team player.