According to Sportitalia (via Robert Summerscales of MailOnline), Hysaj has a €50 million (£43.7 million) release clause in his contract at the Stadio San Paolo, a more than affordable fee for the Premier League trio.
The report added the Blues are in pole position to sign the 24-year-old as they have already met several times with the Albanian's agent.
Unlike Liverpool and United, though, it is not looking likely that Chelsea will be able to offer Hysaj UEFA Champions League football next season, which could work against them.
Hysaj has started 31 of Napoli's 34 Serie A matches this season, including the Partenopei's 1-0 defeat of Juventus on Sunday that saw them move to within a point of the table-topping Old Lady with four matches of the 2017-18 campaign remaining.
In the main, he has been utilised on the right side of the defence, but he has also sporadically taken up the left-back role while Faouzi Ghoulam has been sidelined.
His versatility is likely one of the key reasons he has caught the eye of Chelsea, United and Liverpool, along with his relatively affordable price tag.
Meanwhile, Hysaj also boasts many of the attributes required of top modern full-backs, combining defensive acumen with attacking intent.
Maurizio Sarri, one of the Europe's most highly regarded managers, has trusted him to act as a starting full-back for both Empoli and Napoli since he was 18.
Hysaj's skill set, experience and potential to improve even further could make him a fine addition in the Premier League, and it would be little surprise to see Chelsea, United and Liverpool fighting for him in the summer.