ESPN reported on Thursday that the Brazil international midfielder -- who has won five Champions Leagues and three LaLiga titles in nine years at Madrid -- was considering an offer from United, with a decision imminent.
Casemiro, 30, is expected to receive a substantial pay increase at United, who have been looking to strengthen their squad after losing the first two games of the Premier League season.
"I talked about it with [Casemiro] this morning," Ancelotti said in a news conference on Friday ahead of Madrid's LaLiga game at Celta Vigo. "He wants to try a new challenge, a new opportunity. The club and I understand it. Casemiro -- with what he's done at this club, and with the person he is -- we have to respect this desire he has.
"There are negotiations right now. Nothing is official, he's still a Real Madrid player, but he wants to leave. If he goes and reaches an agreement, we have the resources to replace him."
Ancelotti said he had not tried to convince the player to change his mind.
"I just listened to him," the Italian coach said. "Hearing his desire to leave, there's no way back ... If the negotiations go well and an agreement is reached, we have to wish him all the best and look at what we have.
"It's hard to speak now, because we don't know what will happen in the next few hours, whether he stays or goes. But if he goes, we're hugely grateful to him."
Ancelotti said the club would not look to bring in an additional midfielder if Casemiro completes his move to United.
"We have replacements within the squad," he said. "We have a lot of good players who can play in that position. Tchouameni is one of the best midfielders in the market right now. Then there's the option of Toni Kroos, who can play in that position, as he did in my second year here [the 2014-15 season], when we won 22 games in a row.
"We have [Eduardo] Camavinga, who played last year. We can't replace Casemiro with a player with the same characteristics, but we have others with different characteristics ... In my [AC Milan] team [Andrea] Pirlo played in that position and did well."
"If Casemiro goes, we have six midfielders," Ancelotti added. "[Luka] Modric, Kroos, Tchouameni, [Fede] Valverde, Camavinga and [Dani] Ceballos. I think six are enough to manage all season."