That’s according to Marca, following Inter Milan’s interest in Modric.
The Croatian midfielder has been targeted by the Serie A giants in recent weeks with a lucrative €10million-a-year (£9m) contract offer supposedly lined up.
Inter’s offer is believed to include two years at Jiangsu Suning with the Chinese Super League club belonging to the same owners as the Italian outfit.
Modric is recognised as one of the best midfielders in the world, if not the best, having been awarded the Golden Ball at the recent World Cup in recognition of his role in Croatia reaching the final.
The 32-year-old, who turns 33 next month, is also in the running for the Ballon d’Or this year having been crucial to Real’s third successive Champions League triumph last term.
Inter would be a surprise destination having not won a trophy since 2010-11, failing to finish any higher than fourth in the Serie A in the years since then.
But Modric is believed to be seriously interested in a move to the San Siro, where he would join up with compatriots Ivan Perisic, Marcelo Brozovic and Sime Vrsaljko.
Reports in Spain indicate that Modric – who returned to training yesterday – wants to evaluate Real Madrid’s response to Inter’s interest.
And according to Spanish outlet Marca, it is highly likely that Madrid will offer Modric a substantial improvement to his current pay-packet as an incentive to stay at the Bernabeu.
It is believed Modric will hold talks with Madrid president Florentino Perez today or tomorrow to discuss his future – with the transfer window not closing for Spanish or Italian clubs until August 31 although it closes for English clubs at 5pm this evening.
Perez declared recently that the only way for Modric to leave would be for a club to meet his €750m (£676m) release clause.
The former Tottenham star would follow in the footsteps of former Real Madrid talisman Cristiano Ronaldo by swapping Madrid for Serie A.
Ronaldo joined Juventus in a mammoth £88.8m deal last month to end a nine-year stay with Los Blancos after personally requesting to Perez that he sanction an exit despite a €1bn (£901m) buy-out clause in his contract.
Marca add that Inter have been encouraged enough to believe a deal is viable although it is widely expected Modric will be tied down to fresh terms in the Spanish capital.
And while the player’s standing has not suffered as a result of the situation, it’s claimed there is basement in the higher levels of Madrid’s hierarchy that neither Modric or his representatives have denied the rumours or spoken of the player’s commitment to the La Liga heavyweights.
The situation is all the more pressing for Madrid with Ronaldo having not been replaced.
They added Thibaut Courtois from Chelsea to their ranks yesterday for around £35m, sending Mateo Kovacic to the Blues on loan in return.
Real Madrid have also signed Brazilian whizz-kid Vinicius Junior, right-back Alvaro Odriozola from Real Sociedad and up-and-coming Ukrainian goalkeeper Andriy Lunin.