Reports in the Italian media have stated that United had a scouting delegation at the Stadio Olimpico as Torino took on Roma, and Ogbonna was believed to be the reason for the visit.
Highly-rated Ogbonna has been linked with a number of Premier League clubs over the last 12-months.
However, the 24-year-old Italian international insists he is focusing on making sure Torino stay in Serie A.
"If they came to see me, this obviously flatters me, but right now I don't think about the future," he told Sky Sport Italia.
"I live in the present and, just like all my team mates, I think only to the Torino's salvation."
Ogbonna has spent his entire career with Torino having come through their youth system, and is considered one of the best young defenders in Europe.