The Portugal forward's current deal with Real expires in June 2015, meaning he could leave the Spanish capital in two years on a free transfer.
Throughout the summer, Real president Florentino Perez has reiterated his desire to hand a new contract to Ronaldo and repeatedly insisted his belief that the 28-year-old will put pen to paper.
However, the lack of an official announcement about the deal, with the new season less than a fortnight away, has fuelled speculation that the player is not going to sign a new contract at all, as part of a ploy to return to Old Trafford.
In a press conference on Sunday evening, Ronaldo gave no clues away about his intentions, simply remarking that "the situation still hasn't been resolved".
But, speaking at a press conference in Miami, Ancelotti expressed confidence that Ronaldo and the club would finalise a deal soon.
"The player wants to renew his contract and the club want him to renew it too, so I don't think it's going to be a problem," the Italian was quoted as saying by Madrid-based newspaper AS.
"I think Cristiano and the club are relaxed about the issue. I don't know when it will happen, but I am certain that Cristiano is going to renew his contract with Madrid."
Real will lock horns with Ancelotti's former club Chelsea on Wednesday night in Miami in the final of the Guinness International Champions Cup - a match which also sees Blues boss Jose Mourinho face his old club just two months after leaving the Bernabeu.
Mourinho left Madrid in a cloud of controversy, making negative remarks in his final weeks in charge against club captain Iker Casillas, defender Pepe and Ronaldo, who he said "maybe thinks that he knows everything and that the coach cannot improve him any more".
In a recent interview with ESPN, the 50-year-old made another disparaging remark against his former player, saying that "the real Ronaldo" was the former Brazil striker, not his fellow Portuguese.
He also criticised his former club, saying: "Madrid is politics, Madrid is not about football."
Wednesday night's game has been billed as a grudge match in light of Mourinho's remarks, but Ancelotti sought to cool the tension.
"We are playing a match against a strong team, not against Mourinho," he said.
"For us, it's very important that we play well and give our all. We have to try and improve our fitness too, because the season starts soon.
"It's a special game because I spent two years at Chelsea. I had a very good relationship with all the players and with the supporters there.
"It's a very important pre-season game because we are up against a strong team and it'll be a good test to see what our fitness is like after all the work we have done."