Koulibaly, 31, is believed to be edging closer to completing a permanent switch to Stamford Bridge, with one report claiming that the Blues have made significant progress in their £33.9m pursuit of the Senegal international.
According to journalist Alfredo Pedulla, via The Sun, Napoli have opened talks with Man United over the availability of Bailly, who has two years remaining on his contract at Old Trafford.
Bailly, who has also been linked with Fulham, is currently away with Erik ten Hag's squad in Bangkok and played in United's 4-0 victory over Liverpool on Tuesday.
The Ivory Coast international is set to travel with the rest of the squad to Australia for three more pre-season friendlies, but his involvement with the Red Devils could be cut short should progress in negotiations with Napoli reach an advanced stage.
Bailly, who has spent the last six years with Man United, was a peripheral figure at Old Trafford last season and featured only seven times across all competitions.