Both Manchester giants will reportedly go to war over the West Ham United defender.
Along with a number of Slaven Bilic's summer signings, Ogbonna has enjoyed a stellar first season in the Premier League, starting 16 matches following an injury earlier in the campaign.
The 27-year-old's physicality has reportedly won him some admirers at Old Trafford, with the Red Devils' hierarchy said to be keen on adding him to the squad during the off-season.
United have been decimated by injuries to defensive personnel this season, with Matteo Darmian, Phil Jones, Matteo Darmian, Chris Smalling, Antonio Valencia, Luke Shaw currently out of commision.
City's reported interest is also understandable, given how shaky Manuel Pellegrini's side look without the presence of captain and centre-back Vincent Kompany back there.
The Citizens have dropped plenty of points this season due to errors from the likes of Martin Demichelis and Eliaquim Mangala and, with Kompany often sidelined, they need a rock-solid figure at the back.