The 29-year-old centre-back had reportedly become a transfer target for the Giallorossi, who are eager to strengthen their defensive options before the transfer deadline next Monday with the Cameroonian – who played 38 times, missing just three games in all competitions last season for Torino – appearing to be a solid option to replace Kostas Manolas.
Nkoulou is said to have told Torino boss Walter Mazzarri that he wanted to be excused from Sunday's Serie A opener against Sassuolo as he felt unable to focus amid the speculation over his future. He was not involved in the 2-1 victory.
Cairo was furious with the Cameroon international after the match but insisted he did not want to sell the him and said there was a written agreement with Roma that would see them penalised if they contacted any Torino player about a transfer.
However, in a statement released on Monday, Roma said: "In reference to the recent comments made by the president of Torino FC, Urbano Cairo, and reported by a number of media outlets, the club would like to clarify that it has never made contact with any Torino player and is not interested in any member of the Granata squad."
Cairo had said to Tuttomercatoweb: "I said at the beginning of the transfer window that I will keep everyone, so he [Nkoulou] will also stay.
"Maybe he has other ideas, but he has a contract for another two years. Nkoulou must apologise to the club and to his team-mates.
"I even met with his agent at Forte dei Marmi: we were talking all afternoon and even talked about adding a buyout clause [to his contract].
"Roma aren't even able to contact our players: there is a written agreement that, if they do, they have to pay a penalty of €900,000."
Torino's next game is against Wolverhampton Wanderers in the second leg of a Europa League qualifier, having lost 3-2 at home in the first leg.