Ogbonna plays his club football for Torino, and is rated as one of the best defenders in the Italian top flight.
And his performances this season have attracted the attentions of Liverpool and Manchester United, although Roma are also thought to be tracking the Italy international.
Gianluca Petrachi, Torino's sporting director, admitted Roma submitted an enquiry over Ogbonna in the summer, but a deal was not reached.
Liverpool and Manchester United have now joined the hunt, and Petrachi confirmed Ogbonna is in demand.
Speaking to Teleradiostero, and quoted on talkSPORT, Petrachi said: "Roma made an enquiry, but they never made us an official offer.
"Ogbonna is wanted by a lot of teams, but it would be reductive to name them all at this moment in time.
"Strong centre-backs are always requested by many sides."
The 24-year-old came through the Torino academy, and has five caps for Italy. Although he was named in Cesare Prandelli's national team squad for Euro 2012, he played a minimal role as Italy reached the final only to lose 4-0 to Spain.
Manchester United have suffered a defensive injury crisis this season, with Nemanja Vidic, Chris Smalling, Phil Jones and Jonny Evans all spending time on the treatment table, but Liverpool could still rival the Old Trafford club in January as Brendan Rodgers could look to strengthen his defence.