It is also suggested that the arrival of Higuain will see the door firmly opened for Alvaro Morata to depart.
Higuain knows Sarri well as he played under him during their time at Napoli where the striker arguably played his best football having scored 91 goals in just 146 games during a three-year spell at Stadio San Paolo.
Higuain's current sporting director has challenged his striker to improve at Milan, with a move to Stamford Bridge looking increasingly unlikely.
Higuain had his most successful season under Sarri, breaking the Serie A goalscoring record with 36 goals in the 2015/16 campaign.
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Higuain joined Milan on a season-long loan from Juventus in July with an option to buy but has struggled to settle at the San Siro, scoring eight goals in all competitions.
The Argentina global has managed just eight goals in 20 appearances in all competitions, well off his best scoring rate during his time at Napoli and Juve.
"A goal can change things, but if he is to continue here, he needs to take on responsibility", he said.
Morata - who has netted only 16 goals in 47 league appearances since his £60m switch from Real Madrid in 2017 - is linked with a move to Spain with Sevilla apparently keen on the former Real Madrid forward. Seeing as he is here, he needs to get down and actually do something for this team.