The Croatia international was linked with a move to Chelsea last summer, but Spurs chairman Daniel Levy kept him at the club despite the player's apparent discontent. After four years at White Hart Lane, Modric now looks to be on his way to the Spanish champions, who have pursued the deal with some vigour this summer.
"Daniel Levy promised a year ago that if an offer from Madrid arrived he would let him go," said the Croatian coach Igor Stimac to Spanish newspaper AS.
"And when the offer arrived he changed his opinion. I think that this guy tries to make himself famous in the world of football, but this isn't the way to do it.
A figure of £23.6 million has been touted with add ons bringing the total transfer up to around £27.5m.
Modric has never hidden his desire to join Jose Mourinho's side with various media outlets now claiming a deal could be completed before the La Liga season begins this weekend.
New Tottenham manager Andre Villas-Boas criticised Modric after he did not travel to the United States for the club's pre-season summer tour. The 26-year-old has continued to train away from the rest of the squad, He could now be involved when Real Madrid open their Spanish league campaign against Valencia at the Bernabeu on Sunday.
Villas-Boas has strengthened his midfield with the signing of Gylfi Sigurdsson since replacing Harry Redknapp as Tottenham coach. He will have money to spend on new faces before the end of August if Modric moves on with attacking midfielder Joao Moutinho touted with a move to rejoin his former Porto manager in London.