Goal understands Los Blancos president Florentino Perez has made Bale his No.1 target and is willing to offer him a mammoth £200,000-a-week to entice him from White Hart Lane to Santiago Bernabeu.
Tottenham expect Bale to remain at the club and have offered him a new deal worth £130,000-a-week, but Modric believes his former Spurs team-mate would make a huge impact in the Spanish capital.
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"A club like Real Madrid, Tottenham or anyone else can only benefit from having a player like that.
"As Real Madrid is a team of stars, Bale would fit perfectly. He would give us a different dimension.
"If he signs or not is a matter for the clubs, but if he ends up at Real Madrid that can only be good for us.
"As Real Madrid is a team of stars, Bale would fit perfectly. He would give us a different dimension. He can shoot, has strength and speed and is the type of player who could help us take a step forward."
Modric also took the opportunity to dispel reports he is unsettled in Spain and is considering a return to the Premier League this summer.
"I have no doubt [I will stay]," he insisted. "I want to remain at the best club in the world.
"It is a privilege to be here. I want to show more in the future and I am not thinking about anything other than continuing here next season.
"I think Real have only seen a little bit of my game. I can perform better and offer more. In the future I hope to do that and prove to the club and the fans that they were right to bring me here.
"I want to make sure that I have a good pre-season and prepare well for next season. That is important to me."