Juventus want to make Sarri, who won his first major trophy as a manager on Wednesday night when his Chelsea team lifted the Europa League in Baku with a 4-1 hammering of Arsenal, their next manager after Massimiliano Allegri left at the end of the season.
The Serie A giants are offering Sarri, 60, a £6.2million-a-year three-year deal – but have not yet made an official approach to Chelsea.
Sarri, as well as winning the Europa league steered his side to third in the Premier League, clinching Champions League football for next season, and reached the Carabao Cup final – but his future is still uncertain.
After the win in Baku, Sarri indicated that he might well now be thinking about staying, as he said: “I am starting to feel like this Chelsea team is mine.”
And Brazilian defender David Luiz demanded that Chelsea should do everything in their power to keep Sarri at Stamford Bridge: “Yes. He’s doing great. He did great during the season even with all the difficulties we had.
“It’s his first season at Chelsea, his first in English football. He is a great person, a great guy, a great manager and we finished in the best way for him because we finished winning a trophy in his way.
“Even after we conceded a goal at 3-1 we continued to play his philosophy and continued to try to score more goals. It was the best end of the season for him and he deserved that.
“It is for the club to decide, but I am so happy with him. Sometimes we are with the guys we work with more than our families. We make connections. Maurizio did that with us. He has some connections with us, that’s why he loves this group.
”The criticism is normal. It proves that Chelsea is a big club. In life sometimes you have to try to understand who is on the other side.
“You need to reflect and analyse how difficult it was for him to be here today. He was doing one job (as a banker) and then he quit to try a big journey and do something in football.
“He was training many clubs in the Italian lower divisions. Now he arrives in a big final and to do great like that, of course, there is going to be emotion.
“For us, it’s emotional too. He deserved that, it was a fantastic season for him.”
It has though not always been an easy season, with Sarri until now not connecting with Chelsea’s fans, who at one stage called for him to be sacked.
The club were understood to be ready to let the Italian go if Juventus paid up the £5m they want for the remainder of his contract.
Express Sport has learned Sarri is not the only London-based gaffer Juventus have had in their sights as they look for a new manager to replace Allegri.
Mauricio Pochettino, who will lead Tottenham into Saturday’s Champions League final, has also been on the Italian champions’ radar.