Hysaj has fallen out of favour since Carlo Ancelotti's arrival in Naples. The Napoli boss prefers Nikola Maksimovic and Kevin Malcuit ahead of the Albania international, but the 24-year-old remains a favourite of Sarri, with Chelsea's manager having had the player at both Empoli and Napoli.
Still, Chelsea may have to wait until the summer to complete a deal.
SPAL's Manuel Lazzari has been lined up as Napoli's replacement should they choose to cash in on Hysaj, but the deal is complicated by the fact that Chelsea would have to offload Davide Zappacosta to make room for a new arrival.
Lazio are keen on a loan move with an option to buy the former Torino man, who cost Chelsea £23m in 2017. Talks have taken place between the clubs, but an agreement over the end-of-season fee is yet to be reached as the Blues look to recoup their initial outlay.
Napoli could be at the centre of Chelsea's winter transfer hopes as they are in contention to sign £45m-rated Cagliari midfielder Nicolo Barella, whose arrival at Stamford Bridge would allow Cesc Fabregas to complete a move to Monaco.
It is understood that Barella himself is cautious about moving in the winter window, but the decision may be taken out of his hands as Cagliari have already lined up a replacement in Boca Juniors' Nahitan Nandez, for whom a bid has already been accepted.
Chelsea's previous transfer window was also held up by tough negotiations with Napoli. Blues director Marina Granovskaia had to deal with prickly Partenopei president Aurelio De Laurentiis in order to sign Sarri and Jorginho.
Goal can also reveal that Atletico Madrid have joined Sevilla in showing an interest in Alvaro Morata as both clubs look to secure a loan move for the Spaniard, but Chelsea would first need to sign an alternative as they struggle to secure Sarri's first choice in Gonzalo Higuain.
The January transfer window is proving to be rather chaotic for Chelsea, with Callum Hudson-Odoi's situation also up in the air amid a £35m bid from Bayern Munich.