The Italy international recently revealed he was flattered by speculation linking him to Liverpool, but Manchester United are also believed to be keen on the young defender.
The Premier League pair were thought to be scrapping for his signature, but now Serie 'A' giants AC Milan have joined the race. Ogbonna is rated as one of his country's brightest young defensive prospects, and the Torino defender already has four Italy caps.
The 24-year-old was part of the national team squad that manager Cesare Prandelli picked for Euro 2012, as the 2006 World Cup winners reached the final, only to lose to Spain 4-0 in the final.
Milan have endured a difficult start to the Serie 'A' season - they currently lie 11th - and coach Massimiliano Allegri is under pressure to turn it around.
Allegri's side have won just four of their opening seven matches, and their normally resolute defence has looked porous in the season's first few months.
TalkSPORT reports that Allegri could refocus his transfer efforts on solidifying his defence, with Ogbonna potentially a priority for Milan.
But the Italian club are likely to face competition from the Premier League, with Liverpool and Manchester United thought to be monitoring Ogbonna's progress.
United have problems at the heart of their defence. Captain Nemanja Vidic is currently on the sidelines, while Chris Smalling and Phil Jones have been long-term injury concerns. And Sir Alex Ferguson could look to Ogbonna to provide cover for United centre-back Rio Ferdinand - a player who has had injury troubles of his own in recent seasons.
Liverpool look relatively secure at the back, but Brendan Rodgers is believed to be keen on the young defender. The Anfield club already have Martin Skrtel and Daniel Agger, so the Reds could choose to focus their efforts elsewhere in January.