TMW says Inter and Modric's camp have settled on a three-year contract for the Croatia worldwide.
Kovacic also helped force his move away from Madrid before the end of the transfer window by refusing to continue with pre-season training until his future is resolved.
However, newly-appointed Madrid boss Lopetegui has echoed the words of Perez and dismissed any talk of losing Modric.
"I think the president said it, I don't think there's much more to add", the manager told a news conference, according to FourFourTwo.
"We are calm and counting on him, we hope he returns to enjoy Madrid, I have no doubt that he will stay", Vazquez said.
Baby's body pulled from water near Brooklyn Bridge
The baby boy, thought to be about 8 months old, was transported to a local hospital where he was pronounced dead. No parent or guardian was present at the scene and the child showed no signs of trauma, police said.
He also enjoyed a stellar World Cup campaign with Croatia, inspiring their run to the final - where they lost 4-2 to France - and claiming the Golden Ball as the tournament's best player.
Real are yet to replace Cristiano Ronaldo following his £105m move to Juventus, but Lopetegui is confident the club will cope without the five-time Ballon d'Or victor.
"Well, you never know in football, but I think that Luka is a Real Madrid player and will continue to be so".
Real Madrid have identified Luka Modric replacement.What's the rumour? "Luka Modric is an extraordinary player and we're waiting for him with open arms".
Inter want to take Modric on-loan for a year with the option to buy.