The 20-year-old Ghanaian international has made 28 appearances for Augsburg in the Bundesliga this season and has picked up four assists.
Chelsea are now hoping to beat City to the services of the pacey wing-back as Filipe Luis is looking likely to depart less than a year after joining the club, with a return to Atletico Madrid a real possibility.
Cesar Azpilicueta has established himself as the starting left-back at Stamford Bridge and has had an excellent season for the new Premier League champions.
But if Luis departs, a backup left-back will be needed, and Baba could be an ideal acquisition at such a young age.Embed from Getty Images
The Ghanaian has four years left on his current deal and would cost around £11 million as the Blues look to bolster their squad early this summer.
City have been linked with a move for the emerging star as they look for a new left-back too. Danny Rose has also been linked with a switch to the Etihad as Gael Clichy and Aleksandar Kolarov are deemed not good enough by Manuel Pellegrini.
Would Abdul Rahman Baba be a good signing for Chelsea? Do the Blues need another left-back?