The defender was rumoured to be the subject of a €10-million bid from the Lupi earlier in June, which was allegedly dismissed by Blaugrana boss Luis Enrique.
However, Affonso, though careful not to overstate Roma's interest, suggested there are numerous potential opportunities for his client to consider and stressed that his future may lie away from Barcelona.
"For now we have not been officially contacted by any club," Adriano's agent told Corriere dello Sport.
"Reports of Roma's interest have come to us from the newspapers. Roma are a great team. But so are Inter Milan, Juventus, AC Milan and Napoli.
"Italian football can boast many competitive teams, where all players would like to play. With Roma, in particular, there is great value [in a potential move]. We know Walter Sabatini, who is doing a great job, well.
"In Italy, however, there are at least five or six other really ambitious teams with important players. A hypothetical interest on the part of all these club is always a source of pride. "
Adriano has played 143 times for the Catalan giants since joining from Sevilla in July 2010, and Affonso admitted that the 29-year-old has yet to fully discuss his future with the club, though Enrique is keen for him to stay.
"I have not talked about the issue with either Adriano or with Luis Enrique," he added.
"But I know for a fact that the new coach is counting on Adriano for the new project. This does not mean, however, that we have closed the door to any proposals.
"We are open to discussion and dialogue with those who want to talk to us. Adriano has played in Spain for ten years, and perhaps it is the right time to experiment in other leagues."