The Brazil international, who is reported to be a top summer transfer target for both clubs, confessed that such speculation has given him an ego boost.
"Those links massage the ego, it cannot be denied," Alisson told Globoesporte. "People get satisfaction when you are being recognised by any club.
"I am very happy to have this recognition, that says to me that I am doing my work well and they are noticing.
"I'm focused on things at Roma, but it is especially nice when we are talking about Real Madrid. And as I said, it does not affect what I have been doing on the field and in my income for Rome, because I am very focused on this moment.
"But I am happy, yes, for the recognition of all."
Earlier this week, it was reported that Roma have turned down a £35m bid for Alisson from Serie A rivals Napoli.