The Croatia international has been linked with a move to Serie A giants Inter Milan.
Modric is yet to return for pre-season after an impressive World Cup campaign, but Lopetegui has calmed the nerves of Los Blancos supporters.
"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.
"He's made it concise and clear. Luka Modric is an extraordinary player and we're waiting for him with open arms
"I talked to Modric after the great World Cup that he had. We will see him when we get back on August 8 and we'll see if he is available on the 15th in our first key match.
"What I told him is ultimately private but what I feel is that he's a player that I love watching and I'm thrilled to have him, and ultimately I think he'll be very happy to be on the team.
"He is our player… We've been able to enjoy watching him play and we will continue to enjoy watching him."