Both Manchester United and Liverpool are said to be monitoring the progress of the Napoli fullback but it is Chelsea who is leading the race right now. The Blues are reported to be the closest to sealing a deal as they claim Hysaj's agent has met Stamford Bridge chiefs in person on multiple occasions.
Hysaj is a versatile player who is most comfortable at right back but has shown he can fill in wherever there are gaps. The former Empoli star has played six of his 38 starts for the club at left back after the injury to Faouzi Ghoulam.
Chelsea are in the market for another right back with boss Antonio Conte switching between struggling duo Victor Moses and Davide Zappacosta. Zappacosta has failed to cement his place in the squad in a disappointing debut season in West London whereas Moses has also seen a dip in his form after a brilliant last season.
Manchester United boss Jose Mourinho is also looking for a new right-back and a new left-back and Hysaj, thanks to his versatility, has caught the eye of the former Chelsea boss.
But Liverpool are the team who seem to have the least need for Hysaj with youngster Trent Alexander-Arnold, Joe Gomez and Nathaniel Clyne all playing on the right this campaign. The Reds also have two pretty decent options at left-back with Andrew Robertson and Alberto Moreno.
Chelsea are likely to part ways with Antonio Conte at the end of the season following an unconvincing season but they have already started looking for reinforcements.
It is not yet decided who will take over as the next manager but plenty of names have been linked including Brendan Rodgers, Luis Enrique and plenty more.
Conte plays in a rather unique 3-4-3 system and whoever takes over as the new boss, will have to work a lot on his squad to mould them into his new system which might take some time.