Di Maria, who was kept at the Santiago Bernabeu in the summer in preference to Mesut Ozil by coach Carlo Ancelotti, is under contract with Real until 2018.
And Monaco coach Ranieri is not expecting the Argentina international to be the latest expensive and high-profile recruit to his squad in the New Year.
"Indeed, he is a player I am interested in," Ranieri told reporters after Monaco’s 1-0 win over Ajaccio on Sunday.
"But I don’t think he will join us. It is just rumors."
Meanwhile, speculation continues to surround the future of Radamel Falcao after the striker was again absent for Monaco against Ajaccio.
The Colombia international has been carrying a thigh injury, but Ranieri hopes Falcao could return to face Guingamp at the weekend after appearing to grow frustrated by the constant rumours surrounding the player.
Ranieri added: "Maybe he will play. We will see on Wednesday if he can have a whole training session with the group.
"Even if I tell you no, there is no Falcao problem, you will write ‘yes’, so write what you want."