The 25-year-old defender has been heavily linked with a move away from Torino this summer after a series of impressive performances in Serie 'A' in 2012/13.
Manchester United have been credited with an interest in bringing the Italy international to Old Trafford, but David Moyes will face a fight to secure Ogbonna's signature, after Antonio Conte prepared a player-plus-cash bid for his services.
Juventus will offer £10million and Paolo De Ceglie in part-exchange for the centre-back, who is rated very highly by a number of different sides across Europe.
The Turin-based club want an answer from Torino in the next few days, meaning Manchester United will have to move quickly if they plan to lodge a rival bid in an attempt to lure Ogbonna to the Premier League.
According to Italian publication Gazzetta dello Sport, the two clubs will resume talks about the prospective transfer on Tuesday, as the Bianconeri look to usurp rival suitors by agreeing a deal in principle for Ogbonna before the transfer window reopens on July 1.
Stadio Olimpico until 2016, but as he looks to cement his place in the Italy squad ahead of the 2014 World Cup in Brazil, he might look favourably upon a move to a bigger club ahead of the new campaign.Ogbonna is under contract at