The Tottenham Hotspur midfielder has long been linked with a move away from White Hart Lane, and with the Lilywhites failing to secure Champions League football, could be set for a move this summer.
The 44-year-old believes Modric has the ability to play at the highest level and has urged Blancos' coach Jose Mourinho and president Florentino Perez to consider singing the diminutive playmaker.
"As a future president of Croatian football, I'd love to see Luka Modric join Real Madrid," he told Marca.
"He has the quality and the ability to play for a big club like Real. But it is a question I will pose with my heart to Mourinho and Perez."Suker will present the Man of the Match award at Saturday's Euro 2012 quarter-final between Spain and France and ahead of the clash he has picked Spain to triumph and tipped Fernando Torres to make the difference.
"Of Spain's strikers the one I like most is Torres, because he is fresh. I hope he scores a double tonight to qualify for the semi-finals.
|2/1||A Germany versus Spain final at Euro 2012 is 2/1 with Paddy Power|
"The good thing for Spain is that he hasn't played so much for Chelsea and can be at his maximum level tonight.
"I am sure [Andres] Iniesta will be good, while I also like the defence and Iker [Casillas] is tremendous. I am sure we are going to see a great game."
The former Real Madrid and Arsenal striker has put his money on a Euro 2008 final re-match between tournament favourites Germany and Spain.
"I hope Spain win. I give the prize to the best player and I hope it's a Spaniard. I am convinced that Spain will play well. They are hungry. And I expect to see a Spain v Germany final in Kiev on July 1."