Suker, who played for Madrid between 1996 and 1999, claims that joining the Spanish champions would be the "best move" of the 23-year-old's career.
"If he has the possibility to go to Madrid, it would be his best move of his career," he told BBC Wales.
"So many clubs in the world have huge histories. Arsenal is a great club, Manchester United and Chelsea.
"For me Real Madrid is one of the best clubs in the world."
Bale's current contract with Tottenham runs out in June 2016.