The Spanish striker has struggled to adapt to life in the Premier League and appears to have lost the confidence of Sarri.
The deal could now be finalised "in the coming hours", as Chelsea are willing to pay Higuain's salary, as well as a potential €40million (£36m) transfer fee to make the loan move permanent in the summer.
However, Milan sporting director Leonardo warned on Tuesday he had to get down to work.
"Gonzalo has lived through this moment but now he has to leave it behind him".
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.
"A goal can change things, but if he is to continue here, he needs to take on responsibility", he said.
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"But with all the rumours, there is no point in me thinking about these different situations until we have something to answer".
"He is here right now". Seeing as he is here, he needs to knuckle down and actually do something for this team.
Higuain's had a nightmare term thus far.
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.
Chelsea's strikers aren't doing too good this season, either.