The Blues, however, are waiting on the outcome of their appeal to the Court of Arbitration for Sport over their FIFA transfer ban to discover if they can make a move.
But The Mail are reporting that Chelsea are keen on Bailey, who will cost around £80million.
The 21-year-old would fit the dynamic winger mould that Chelsea will be after following Eden Hazard’s departure.
The Belgian has joined Real Madrid for £88m with the fee likely to rise to £130m.
Ageing forwards Pedro and Willian are coming to the end of their time with Chelsea and the club will be looking revive their front-line with fresh talent.
Callum Hudson-Odoi is yet to come back from an Achilles tendon tear but will probably take up a starting position on the opposite flank to Christian Pulisic.
Pulisic was bought in January for £57m from Borussia Dortmund but will link up with his new team-mates this in the coming weeks.
Bailey was a hot transfer topic among English clubs last summer but the Jamaican endured a tough season with Leverkusen.
Leverkusen might be reluctant to sell, though, having already shifted star player Julian Brandt to Dortmund.
Chelsea are also enquiring about the availability of Ajax’s David Neres, who Arsenal are have been tipped to sign.
Bailey scored just five goals and assisted once, in contrast to to the previous season where he notched nine times and laid on a further six for his team-mates.
The decision on transfers will not only wait until Chelsea’s FIFA ban is sorted – but also until they appoint a new manager.
Current boss Maurizio Sarri is expected to leave next week following a reported completed deal with Juventus.
The Italian steered Chelsea to a third-placed finish and Europa League glory but failed to warm to supporters with his supposed attacking style of football falling by the wayside.
Sarri only joined Chelsea last summer but it’s also thought that the 60-year-old wants to return to Italy.
Chelsea midfielder Jorginho recently stated that Napoli fans might see Sarri’s Juve appointment as a “betrayal”, having managed the Naples side for three years previously.