Speaking after Madrid's 3-1 win over Juventus in the International Champions Cup on Saturday, Lopetegui pointed to Perez's statement as definitive.
"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.
I talked to him after his excellent World Cup and we'll see if he can play on August 15 (against Atletico Madrid in the European Super Cup), our first big objective of the season. Luka is a Madrid player and will continue to be, I have no doubt.More news: Barcelona rope in midfielder Arturo Vidal
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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.
'I told him he was a player I'm passionate about, I love him and he knows it.
Luka Modric is now 32 years old the Los Blancos are looking for a midfielder who can replace him in their starting line up.
Reported Tottenham target is desperate to move on from Real Madrid.
Inter want to take Modric on-loan for a year with the option to buy.