Beckham seems likely to have played his final professional game after the emotional farewell he received while skippering PSG against Brest on Saturday night.
Beckham could theoretically feature in his team's final match of the season at Lorient, but the events of Saturday night appear to make that prospect unlikely. Lorient also play on an artificial pitch and Beckham admitted on Saturday that he does not like playing on such surfaces.
He will not be short of offers from inside and outside football and whilst Beckham has never been expected to start a career in management, Ancelotti believes it is a possibility.
"Today he finished as an old player, tomorrow he will be perhaps a young manager," the Italian said.
"I'm proud of having coached a great player and professional who gave a beautiful image to the game of football. I respect him.
"It was the right thing to do to choose Beckham as captain for his last match," he added.
"All the players backed the decision. Beckham will have a lovely memory of this night."