City's back line has proved their Achilles heel this season and the Villarreal defender has been targeted to address that, according to the Mirror.
City have conceded the most goals of any of the top four this season (32) after struggling to keep captain Vincent Kompany fit.
Fellow centre-backs Nicolas Otamendi, Eliaquim Mangala and Martin Demichelis have all flattered to deceive in the Belgian's absence, with the latter is set to depart at the end of his contract.
And the tabloid claims Bailly is a target for incoming boss Pep Guardiola, having been recommended to the Spaniard.
Bailly, a 12-cap Ivory Coast international, has appeared 20 times in this season's La Liga - helping Villarreal to fourth in the standings.
And the 21-year-old played the full 90 minutes as Marcelino's side beat Sparta Prague 2-1 in last night's Europa League quarter-final first leg.
According to Transfermarkt, the Yellow Submarines paid £4.28 million to acquire Bailly from Espanyol in January last year.
Another Belgian defender, Jason Denayer, is set to return to the Etihad Stadium when his loan to Galatasaray expires this summer.