Reports in Spain have claimed that Monaco are planning a £29.3m offer for the Argentine, who has also been linked with Arsenal and Manchester United.
Los Blancos boss Carlo Ancelotti rates Di Maria highly, though, opting to keep hold of him in the summer and instead sell Mesut Ozil, and Ranieri is seemingly resigned to defeat in his desire to sign him.
"Indeed, he is a player I am interested in," Ranieri told reporters after Monaco's 1-0 Ligue 1 win over Ajaccio on Sunday.
"But I don't think he will join us. It is just rumours."
Di Maria, 25, has scored four goals in 14 Madrid appearances in all competitions this season.