Perez did not give any details about the deal but the midfielder is expected to sign a one-year contract extension as is the club's policy with players over the age of 30. The Croatia captain becomes a free agent this summer.
"Modric has signed or [rather] we have reached an agreement," Perez told Spanish radio show El Larguero. "With Modric we have had an agreement for some time."
Perez, meanwhile, said that the situation of Sergio Ramos' contract has yet to be resolved.
The Spain and Madrid captain has yet to sign a new deal with his contract expiring this summer. Ramos, 35, has been offered a contract extension but Perez said the situation is different to Modric's.
"Clearly, it's not in the same situation," the Madrid supremo said.
Asked why no agreement had been reached so far with the experienced centre-back, who has been at the club since 2005, Perez said: "I don't know why we haven't. We have spoken many times. I don't want to blame anyone.
"I love Ramos as though he was my son, I've done for him all that I can. I recognise all that he has done. But you [reporter] are not going to encourage me to pay Sergio Ramos more. The situation is what it is, he knows it, too. Let's complete the season and see what happens.
"Once the season is over, I have to see what will happen next season, which will be worse than this one, if COVID-19 continues."