If the move goes through it would bring to an end a four-year spell at White Hart Lane for Modric, during which time he has developed into one of the Premier League's most impressive performers.
The Croatia international was linked with a move to Chelsea last summer but Spurs chairman Daniel Levy stood firm to keep him at the club.
However, intense speculation resurfaced ahead of the current transfer window and Modric made no secret of his desire to join Real Madrid, with Sky Sports now claiming a deal could be completed quickly.
New Tottenham manager Andre Villas-Boas criticised Modric after he did not travel to the United States for their pre-season tour, and the 26-year-old has continued to train apart from the rest of the squad.
Villas-Boas has already strengthened his midfield with the signing of Gylfi Sigurdsson since replacing Harry Redknapp at the Tottenham helm, while Joao Moutinho has been linked with a move to join up with his former Porto manager.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.