The 24-year-old Italian international was allegedly the subject of a Manchester United scouting delegation in Torino's 2-1 home defeat to Roma at the weekend.
Despite the link to the current Premier League leader, Ogbonna remains coy about his future and says he isn't thinking about any potential move just yet.
"This obviously pleases me, but right now I do not think about the future. I live in the present. I, just like all my teammates, think only about saving Turin," Ogbonna told Tuttomercatoweb.
Torino is currently 15th in Serie A and is eight points clear of relegation after this weekend's defeat. Ogbonna is highly regarded in Italy and has been a key performer for the Serie A club so far this season.
Ogbonna, part of the Italy squad that finished as a runner up to Spain in Euro 2012, made his Serie A debut in February 2007 and has been at Torino for seven years.