The 25-year-old has been the subject of several stories in the Spanish press linking him with a January move to the Ligue 1 club following competition in the team from record summer signing Gareth Bale.
However, Di Maria rejected rumours of a move, telling AS.com after Sunday's 3-2 win over Valencia: "I do not want to go. I want to win my place in the team.
"Not me, nor anyone in my camp, has asked for a new contract.
"What came out was lies.
"I have been through some difficult days. I am just thinking about Real Madrid and I am still working hard. I have to keep going and try to earn a place in the team."