Although they would succumb 4-2 in the final to France, Modric was recognised for his performances by winning the Golden Ball.
And Lopetegui doesn't expect Modric to leave.
The Croatian star, 24, may be familiar to Sarri having spent time in Italy with Inter Milan, but he has found first-team football hard to come by with Real Madrid since his 2015 move to the Spanish capital.
But, shock reports emerged linking Modric with a move away from Spain.
Real Madrid have already endured an interesting summer with Cristiano Ronaldo leaving the club for Juventus and on the face of it, it would surely be a surprise if they let another one of their key players go before the window closes.
The Italian club have offered him a four-year contract worth €10 million euros a year; a €3.5 million increase on what he current earns per year at Real Madrid.
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The Croatian wants to speak with the club and new coach Julen Lopetegui when the squad returns from their USA tour.
The rumour states that Real Madrid have only identified Pjanic as a replacement for Modric if he departs from the Bernabeu.
It is also reported by the Spanish newspaper that the agreement would see Modric spent two years in China with Jiangsu Suning - who share the same owners as Inter - to see him paid €60m (£53.5m) in total over the next six years of his career.
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.
It appears as if everything is doom and gloom at Real Madrid this summer.