The pair appeared to exchange words on the touchline after Ramos was sent off in the 4-1 win over Galatasaray on Tuesday, prompting speculation of a potential departure in light of reports that Chelsea and Manchester City are interested in the Spain international.
However, the Italian says that he enjoys a healthy working relationship with the 27-year-old and, when asked whether or not he would consider selling the defender, Ancelotti said: "No, no, no. Because he's one of the strongest central defenders in the world and we need to keep him.
"I speak to the president (Florentino Perez) a lot and he has never spoken to me about Ramos leaving the club. Everyone knows how important Ramos is.
"I have no problem with Sergio Ramos, and Sergio Ramos has no problem with me. I only told him that he had to avoid getting turned so easily; I was making a tactical point. He made a mistake, but that doesn't change anything. It's normal to make a mistake on the pitch."
Los Blancos, who sit third in the Primera Liga standings, six points adrift of reigning champions Barcelona, host Valladolid at the Santiago Bernabeu on Saturday.