The former Inter Milan star has reportedly been training on his own since his return from holiday - the midfielder had an extended break due to his participation at the 2018 FIFA World Cup in Russian Federation.
How could Real Madrid line up next season after the transfer window?
But it has been claimed that Modric wants out of the Bernabeu outfit with the terms on offer with Inter dwarfing what he is now paid at Real - AS suggesting he would be paid €3.5m (£3.1m) a year extra.
Modric is yet to return for pre-season after an impressive World Cup campaign, but Lopetegui has calmed the nerves of Los Blancos supporters.
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It's killed seven people , including two firefighters who were helping residents evacuate from the affected area. Altogether, the Mendocino Complex Fire has burned 273,664 acres - growing about 70% over the weekend.
However this golden offer from Inter, with a contract until 2024 and with the possibility to later play in the Chinese Super League, remains genuinely tempting for the World Cup runner up.
Madrid are keen to sign the Belgium global, who has failed to return for pre-season training at Chelsea amid the speculation surrounding his future. It's there he will have a meeting with Florentino Perez to discuss his future, although the president won't sell for less than the €750m stated in his buyout clause. He'll be happy with the proposal he receives here.
While reports said the Serie A side had agreed a deal with Bayern Munich's Arturo Vidal, Goal understands the Chilean midfielder is close to joining Real Madrid's La Liga rivals Barcelona.
"You never know in football but Luka is a Madrid player and will continue to be that way".