Casillas’ future at the Bernabeu is in doubt with the club thought to be interested in acquiring Manchester United goalkeeper David De Gea this summer.
Reports in the Italian press claim Roma have already begun talks to sign the veteran Spanish goalkeeper, who is under contract with Real for another two seasons.
However, when asked about Roma’s reported interested, Casillas’ agent Carlo Cutropia said in Spanish sports newspaper Marca: “I have not received any calls.
“The only thing I’ve said in the past is that Rome is a great city and Roma is a big club with a great fan following.”
Roma finished runners-up to Juventus in the 2014-15 campaign and will play in next season’s Champions League.
The Giallorossi are eager to sign a goalkeeper this summer with their current number one, 38-year-old Morgan De Sanctis, under contract with the club for just another year.
Former Roma goalkeeper Franco Tancredi believes Casillas would be a great signing for the Giallorossi.
“I’ve had the fortune of coaching Casillas for a year at Real,” Tancredi told the Italian press. “I would be very happy to see him at Roma.
“Alongside (Gianluigi) Buffon and (Petr) Cech, he has been for some time one of the best in the world and has done extraordinary things.
“Casillas can have three or four more seasons at a great level. He is a goalkeeper that makes a difference. I really hope that he can come here.”
Casillas’ high wages could pose a problem for Roma, with the 34-year-old currently earning seven million euro (??5million) per season.
Argentina goalkeeper Sergio Romero, Emiliano Viviano’s understudy at Sampdoria, has also been strongly linked with Roma.
Romero is currently enjoying a fine tournament with Argentina at the Copa America in Chile.