The Uruguayan has been linked with a switch to this season's Champions League winners and his representative claims that he has a "predisposition for Spain"
The 27-year-old has long been linked with a move to Carlo Ancelotti's side but insisted earlier in May that he is happy to stay at Anfield.
Suarez, who finished as the Premier League's top scorer with 31 goals this season, signed a new contract with Liverpool in December but the Uruguayan's representative says that the forward would favor a switch to Spain if the opportunity arose.
"A year ago he was very likely to leave Liverpool," Alejandro Balbi told Cadena SER of a summer that saw Arsenal push hard for his signature.
"Now I think it is very difficult because he is an idol, although clubs can offer a lot of money.
"If there is such a big offer from Real Madrid, it would be very difficult to say no. Luis Suarez has always had a predisposition for Spain."