Milan are in talks to sign Genoa striker Krzysztof Piątek in his place, while Chelsea remain locked in negotiations to offload Alvaro Morata in a loan move to Atletico Madrid.
The Spain international is hoping to leave the Blues, allowing space for the club to sign Sarri favourite Higuain.
Sarri was the manager at Napoli as Higuain broke a 50-year Serie A goal record, netting 36 times in a single season in 2015-16. And while Sarri does claim some of the credit, he did not want to boil Higuain's success down to one specific reason, noting the setup of that squad was well-suited to Higuain's strengths.
"It's very difficult to say the reason. Sometimes, Higuain did very well. I think that, in that season, he played in a team very suitable for him," Sarri told reporters.
"So every player, I remember, was very involved in Higuain's record. So there are a lot of reasons, I think. Not only the coach, of course.”
Chelsea have targeted a number of Sarri's former players over the course of his stay at Stamford Bridge so far, and Higuain would follow Jorginho in having come back to work with their old boss.
Jorginho was Chelsea's first signing as he arrived in a £57 million ($73m) deal alongside Sarri from Napoli in the summer. The Italy international sits in the base of a three-man midfield and acts as a pivot for his side, passing the ball an average of 98 times per game.
However, Sarri admits that Jorginho has not been at his best in recent weeks and has encouraged him to move the ball more quickly. This comes as he waits for a potential replacement for his previous deputy, Cesc Fabregas, who joined Monaco on a free transfer last week.
“Jorginho played with me for four seasons," Sarri added. "It's very difficult for him to improve more. He played very well for 20 matches, I think. He's the player in the Premier League who has touched more balls [than any other player], I think.
"Now, maybe, in the last two matches he was a little bit tired. He moved the ball a little bit [more] slowly than before. But I think that it's normal. You cannot stay at the top for 60 matches, so it's normal to have a different period, a period when you are not so lucid as usual.
"But it's not a big problem. Of course, it's the reason I said we needed a replacement for Cesc.”
Chelsea are working on signing Leandro Paredes in a deal which could be worth around £30m ($39m) from Zenit , but they have yet to make a breakthrough in their talks. Sarri was asked why can't he switch formations if Jorginho needs to be rested, in lieu of signing a replacement for Fabregas.
“Because we are not ready to change at the moment," Sarri replied. "I can change when we are at 100 per cent in what I want to see. If in 4-3-3 we are at the top, we can try to change. Like in Naples last season, when we played in the last period also in 4-2-3-1.
"But not at the moment. We are not ready. It's very difficult to say a percentage but, in England, it's very difficult to arrive at the top because this one was the first week without three matches since August.
"So, for the first time in the last four months, we had time to try to improve. So it's not easy in this situation to improve a lot in such little time.”
Chelsea have just gone over the halfway point for the season, having registered only an extra point and an extra goal on Antonio Conte's efforts as the manager at this stage last season. Sarri has been implementing a new system which is a far cry from the way Chelsea have typically played under a succession of managers.
“At the moment, the numbers are really very similar," Sarri said. "In the last part of last season, Chelsea didn't do very well. So we have the possibility to improve on that. But I think it's very important to improve from the starting condition of this year.
"I wasn't involved last season, but I am now. I know very well where we started. And I know very well where I want to go. And I know very well that we need to improve a lot. A lot from the tactical point of view, mentally.
"We had problems with reactions to difficulties in the beginning. Now, for the third time, we reacted very well to a difficulty – after Watford, Tottenham and Newcastle – after their goal. Now we have to show we can react from a positive situation.
"In the last matches, when we scored, we lowered the application and attention. So now we have to work just to avoid this. In my first season in Naples, we gained 41 points in the first half and 41 points in the second half, but in Naples the second part of the first part of the season was really very, very good.
"Here it was better in the first part. I think that we will be able to improve. Not a lot, but we can improve. I have to improve first of all my players. (Callum) Hudson-Odoi is improving. (Ethan) Ampadu is improving. I think that David (Luiz) returned to his top level.
"(Ross) Barkley improved. So we are improving. Then there is the market, but the market is useful only if you need one player, two players at maximum.”