Hazard, 32, has made just one LaLiga start and two substitute appearances this season -- in August and September -- despite suggestions from Ancelotti that he would feature more regularly as a back-up to Karim Benzema.
"There is respect between us. But I'm not going to say that [Ancelotti and I] talk to each other, because we don't," Hazard told Belgian broadcaster RTBF. "But there will always be respect. Even if tomorrow he doesn't pick me anymore.
"I must have respect for a guy like Carlo Ancelotti. In terms of what he represents for football, what he has done in his career. There is no problem."
Hazard joined Real Madrid from Chelsea in a €100 million deal in July 2019 but has never hit his Premier League form in Spain, with a series of ankle problems and related injuries hindering his progress.
Despite his lack of football this season, Hazard said he intends to see out his contract at Madrid, which is due to expire in June 2024.
"I would like to stay, I've always said it," Hazard said. "To hope to play. I'm waiting for one thing, to be on the pitch to prove that I still know how to play football. People doubt me, it's normal. I understand very well. But for me, I'm still here next year. A transfer is not on the agenda. But you never know.
"What can make me change my mind? I don't know. The only thing I think about is playing. That's why I don't even think about leaving. Deep down, I think I can contribute something. I feel it. If I do a little, people will trust me again. They might say to themselves that they made a mistake leaving me out. I just need minutes in the legs."
When asked about Hazard's comments in Tuesday's news conference, Ancelotti replied: "The relationship isn't cold. Look. We have to assess two things. Hazard has been very honest. We don't talk much, I don't speak much with him but speaking is also about character, if you get on better with one person or another.
"It's the same with your children, you can speak more with one child than another. That isn't the most important thing, what's important to me is that even though he doesn't play much, he respects me, and I value that a lot, and I respect him in exactly the same way, that's the most important thing for me.
"He isn't playing because there's a lot of competition, he has a player in that position who's doing a lot right now, which is Vinicius."
Ancelotti also hinted that he is prepared to continue working with Hazard next season.
Real Madrid play Liverpool in their Champions League round-of-16 second leg on Wednesday -- Hazard was an unused substitute in their 5-2 first leg win at Anfield -- before Sunday's LaLiga Clasico with Barcelona.