Modric has enjoyed a successful six years at the Bernabeu, while the playmaker has just been named as the player of the World Cup after helping Croatia to their first-ever final.
However, it has recently been claimed that the 32-year-old was pushing for a summer switch to Inter Milan, and a social media post from Ivan Perisic on Friday indicated that a desire to move to San Siro remained the case.
Real have stood firm regarding keeping Modric, however, and according to AS, the player has decided to accept improved terms offered to him by the European champions.
Modric currently has two years remaining on his existing contract, but it has been suggested that could be extended to at least three years with a significant pay-rise.
The former Tottenham Hotspur man has netted 13 times in 245 appearances since moving to Spain in 2012.