According to Spanish publication AS, the new agreement 45-year-old coach with real Madrid runs until 2020.
Madrid coach Zinedine Zidane has options to fill in for Modric at the Camp Nou, with fellow Croat Mateo Kovacic and summer signing Dani Ceballos the most like-for-like replacements if he wants to continue the midfield diamond shape deployed in Tuesday's 2-1 UEFA Super Cup victory over Manchester United. If we think it's going to be easier [without Neymar] then we're wrong.
Asensio joined Madrid from Mallorca for just £3m in 2014 and he's developed in to one of the hottest properties in Spanish football over the past three years.
Real Madrid star Isco has reportedly already put pen to paper on a new contract that includes a whopping release clause.
Whereas Madrid won the league by three points last season, the prediction for this season is that Los Blancos will pip bitter rivals Barcelona to the title despite finishing level on points.
On the tight match at the Philip II Arena in Skopje, he added: "Madrid is a very powerful team and we are happy". I'm happy to be working so well with my staff.
Ronaldo enjoyed a longer vacation than his Real Madrid teammates to fully recover from Portugal's participation in the Confederations Cup in June.
The Spanish global had less than 12 months to run on his existing deal at the Bernabeu and had been sensationally linked with a move to rivals Barcelona as well as Premier League giants Manchester United and Arsenal. And the objectives are always the same: trying to win every single game and every single title.
"Barcelona are Barcelona, we know how they play and their idea of playing will not change".
Barcelona's summer has centered around the loss of Neymar and the club's attempts in the past fortnight to replace him.