Modric will likely leave Tottenham this summer.
According to Croatian website 24Sata.hr, the 26-year-old midfielder has agreed to terms with the Spanish club and could finalize his move in the near future.
"Everything has been resolved. Luka and Real Madrid agree on everything," a source close to Modric has been quoted as saying.
However, Tottenham's asking price of around £40 million is higher than the Spanish champions are willing to pay for his services.
The source continued, "There is a little more difficulty with the position of Tottenham but everything will be solved and will be resolved quickly."
Should another club produce a better offer than Madrid, it's likely that Tottenham would sell the player to the highest bidder.
An insider told ESPN, "...it seems more likely that Modric will be sold if a club comes close to Spurs' asking price."
The arrival of new Tottenham manager Andre Villas-Boas has facilitated Modric's transfer.
The insider continued, "The club have a new manager who wants to buy his own players and the sale of Modric can significantly help in that direction."