The Spanish striker has struggled to adapt to life in the Premier League and appears to have lost the confidence of Sarri.
However, it is understood that Chelsea's chief-executive, Marina Granovskaia, remains unconvinced that Higuain is the answer to their striker problems.
The Argentine frontman bagged a stunning 36 Serie A goals from 35 appearances under Sarri's tutelage in the 2015/16 campaign.
Sarri's preference is to be reunited with Higuain - who enjoyed his most prolific ever season under the Italian - though any deal is complicated by the forward now being on loan at AC Milan from Juventus.
"He had a tough moment, he has to put it behind him and get to work", said Leonardo.
"Milan's sporting director Leonardo has had some very interesting things to say and he says it's up to Higuain now to make a decision".
"There's no point following rumours and gossip".
"He is here right now".
Higuain's had a nightmare term thus far. However, the move relies on Álvaro Morata moving on, with Atlético Madrid interested in taking the striker on loan until the end of the season with a view to buying him permanently in the summer.
Higuain's arrival would reportedly lead to the departure of Alvaro Morata with the Spaniard strongly linked with a move away from West London this month after a disappointing 18 months at Chelsea following his arrival from Real Madrid in 2017.
Though Sarri has Morata, who joined for £60m from Real Madrid in 2017, and France worldwide striker Olivier Giroud at his disposal, the Italian has often deployed forward Eden Hazard in a more advanced role.