Sarri's future at Stamford Bridge remains uncertain, with the Blues still having the Europa League final against Arsenal to play before its 2018-19 campaign is over, goal.com reported.
Serie A champion Juve has also sounded out Lazio boss Simone Inzaghi, while Tottenham boss Mauricio Pochettino continues to be heavily linked with the top job at the Turin club.
Indeed, Pochettino's cousin Daniele has suggested that the Argentine would be interested in moving to Italy and that ‘everyone in the family’ wants to see him take over at Juve.
Sarri, meanwhile, has added to his options for next season with Roma also interested in appointing him as Claudio Ranieri's successor.
And his future at Chelsea remains somewhat in doubt, with the Blues manager having struggled to connect with the club's fans, having been booed and criticized during his short spell at the helm.
There is further frustration at his style of play, while he hasn't been able to convince fans in the media, with Sarri often reluctant to engage in interview situations unless absolutely necessary.
The 60-year-old has also risked the wrath of his owner, Roman Abramovich, after he was critical of the scheduling of the 'Final Whistle on Hate' match, a postseason friendly against New England Revolution that saw Ruben Loftus-Cheek suffer a serious Achilles injury.
Should Sarri leave, Derby County boss Frank Lampard, who has previously stated his ambition to one day take over at Stamford Bridge, is seen as the early frontrunner.
The Blues legend has guided the Rams to the Championship playoff final against Aston Villa in his first year as a manager after finishing sixth in the regular season.