Di Maria has been strongly linked with a move in January, with French giants Monaco said to be leading the chase.
Di Maria's agent even told Argentine radio earlier this week that there was interest, but he implied Perez was stopping a deal.
Eugenio Lopez told Radio de la Red: "He has a contract in place until 2018 and many clubs want him."
"There is a presidential angle to this but I will not talk about it."
Perez, though, has responded to Lopez's quotes by insisting no approach has been made.
He said: "We have not received any offer for the sale of Angel Di Maria. This is the truth of this subject.
"These are things that do not happen but are written about.
"Nobody has told me anything about this situation, I have asked the club if someone has approached us and nobody knows anything."
Real coach Carlo Ancelotti has also insisted that Di Maria is still part of his plans, despite the fact it seems the Argentine is perhaps set to miss out with Gareth Bale seeing more and more playing time now he is fully fit.
"I haven't spoken to Di María nor have I seen any change of attitude from him or from his team-mates," he said.
Di Maria was criticised for his performance in the weekend's draw with Osasuna but Ancelotti insisted that was not a problem.
"Di Maria came on for Bale against Osasuna in order to change the way we play. With Bale we played 4-4-1 & 4-3-3 with Angel," he said.
"Di Maria didn't play well against Osasuna but it doesn't matter."
Meanwhile, Di Maria himself has spoken about how much he learned from previous Real Madrid boss Jose Mourinho.
"Mourinho turned me into a better player, he should me many things and helped me grow as a footballer," said Di Maria.
"He helped me move to a different position and sacrifice more for the good of the team. I am very grateful to him.
"He told me that I was a striker that could also defend and that I couldn't relax when the opponents were attacking."