The 2018/19 Premier League fixtures were released on Thursday but Chelsea have still not decided whether Antonio Conte will remain at Stamford Bridge, after a disappointing 5th place finish last time out.
Maurizio Sarri, who guided Napoli to a close 2nd in Serie A last season before resigning from the post, is among the favourites to succeed his fellow Italian if Chelsea do decide to make a change.
Rugani's links to both managers means that Chelsea can pursue their interest despite the managerial uncertainty. The Mirror understands that a bid of £26m would be enough to secure a deal.
Chelsea's interest in the 23-year-old was the subject of discussion between the player's representatives and Juventus executives in a Thursday morning meeting in Milan.
Rugani joined Juventus from Empoli in 2013 during Conte's reign, though he was quickly loaned back to Empoli and didn't make his Juventus debut until Conte had left the club.
His manager at Empoli was Sarri, who made him a first-team regular with 81 appearances over two seasons for the club.
Conte handed Rugani his first call-up to the Italy senior team in 2016, but he was an unused substitute and didn't actually play for the Azzurri until Conte had been replaced by Gian Piero Ventura.
Sarri is technically still contracted to Napoli despite being replaced by Carlo Ancelotti, but the Partenopei are willing to drop his release clause to £4.5m to encourage Chelsea to pay up.
The Blues would also have to pay £9m in severance to Conte, as he reportedly has no intention of quitting his post.