Higuain has netted eight times in 20 matches for Milan.
The London Evening Standard are reporting on Wednesday that Sarri has once again asked the Chelsea board to try and seal the signature of Higuain.
It is believed that Nicolas will speak to the Blues about a deal, with Juventus wanting the Premier League club to take over the terms they agreed with Milan.
"Higuain must find the real himself, he is living in a different situation for him, he left Juventus and he is here on loan".
"A goal can change things, but if he is to continue here, he needs to take on responsibility".
"He had a tough moment, he has to put it behind him and get to work", said Leonardo. Brazilian Leonardo added: "There's no point following rumours and gossip".
And with the San Siro outfit apprehensive to go ahead with the proposed £36.1million purchase at the end of the season, it's claimed the Argentine has agreed to join Chelsea who it's thought are willing to meet both Juve and the player's money demands. "Seeing as he is here, he needs to get down and actually do something for this team".
The report details that the Argentina worldwide could make the switch to the Premier League in January, as Milan are prepared to cut his loan spell with them.
The 26-yer-old Spaniard has struggled for form since his £65m arrival at Stamford Bridge from Real Madrid in 2017.