Totti, off contract in June, isn't expected to be offered new terms by Roma and has been linked with a move to NASL powerhouse New York Cosmos.
Savarese admits he'd love to bring Totti to the 'States and places the Giallorossi legend in the same category as former Cosmos star Raul. The Real Madrid icon hung up the boots at the end of last season after leading Cosmos to the championship.
Savarese told Tribalfootball.com: "What I can say about that situation is that first of all, I think anyone, any coach, any organization, any club in the world would be interested in a player like Totti, that kind of player that is loyal to an organization.
"It's not many players who can say they spent their entire career with a club and be so successful like Totti has. I think you can talk about Raul and a few other players like Maldini who spent their entire life with the same organization.
"I think he's one anybody would love to have on their team. There has been for sure a contact. There has been a conversation, but that would be the max I'd be able to say right now. We don't like to talk to players who are not our players. He's a Roma-signed player. Definitely there has been a contact, but nothing else."
Savarese says the age of Totti won't be a concern and is no factor considering the success of former Cosmos and Spain international Marcos Senna.
"I always have said the same thing. I don't believe in evaluating a player by their age, but evaluating the player by what he can contribute to the team. I believe Totti is a player who can still contribute to different teams. I think he's always an interesting player, a player any coach would like to have.
"For that, I would say for me age is not a measurement for us to decide if a player has good ability or not. Look at Marcos Senna last year. He was 39 and he gave us everything he had during the entire season and helped us tremendously to able to win a championship."