Beckham seems likely to have played his final professional game after the emotional farewell he received while captaining PSG against Brest on Saturday night.
There remains an outside chance of him being involved in the Ligue 1 champions' last game of the season against Lorient next weekend, but the manner of his 82nd-minute departure at the Parc de Princes - a deafening ovation and warm embraces with numerous team-mates - suggest the former England captain has taken to the field for the final time.
Lorient's artificial pitch seems to be the deciding factor, with 38-year-old Beckham wary of the extra physical demands imposed by such a surface.
The battle for Beckham's services will quickly ensue, with offers sure to flood in from inside football and from every other commercial avenue imaginable.
The daily managerial grind has long appeared an unlikely destination for a man of Beckham's A-list status, but Ancelotti believes it is a possibility.
"Today [Saturday] he finished as an old player, tomorrow [Sunday] he will be perhaps a young manager," the Italian told reporters after PSG's 3-1 win over Brest.
"I'm proud of having coached a great player and professional who gave a beautiful image to the game of football. I respect him."
The scale of Beckham's Paris send-off may have seemed at odds with the fact that he spent just four months with the club, but Ancelotti revealed it was a unanimous verdict from the team.
"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."
Beckham admitted the emotion of the evening will stay with him for a long time, from the distinction of being asked to lead the side to the fact that the match was also a title celebration.
"(It) was a nice way to go out - in front of my own fans, in front of a capacity crowd that were excited because we've won the league. The celebrations have been incredible, so it's a nice way to walk off the pitch,'' he told Sky Sports News.
''To go out like I did tonight [Saturday] couldn't have been any more perfect.
"The manager called me in and said 'we've spoken to the players, it's the players' idea - we want to make you captain'.
''It's really special for an Englishman to be captain of PSG - especially on a night that meant so much to the club and the players. It was an amazing gesture and one I'll always be thankful for.''
Beckham's own words apparently confirmed he had indeed played his last match, but when asked directly he left some room for manoeuvre.
''We'll see. There's a plastic pitch next weekend. I ruptured my Achilles a few years ago, so it's not great for it," he said.
"I'll be part of the team next week. Whether I play or not, who knows?''
Two men who worked with Beckham a long time before Ancelotti - former England boss Kevin Keegan and one-time Manchester United colleague Ole Gunnar Solskjaer - do not see a future for him in the dugout.
Both men are agreed his next footballing assignment could be an ambassadorial one.
"I don't think he really sees that (managing) as being where he wants to go, but you never know," Keegan told Radio Five Live's Sportsweek.
"When you're like David Beckham, he may get an offer at some time that just presses the right buttons. One thing is he'll certainly be able to stand in front of players and they'll listen to him and respect him for what he's done.
"I don't think he wants to do coaching, but if you're talking about being around like Bobby Charlton at Manchester United I suppose, yes, definitely there's a role there."
Solskjaer played with both Beckham and his great friend Gary Neville at Old Trafford.
The pair formed a fine partnership on United's right flank for many years but although Neville has already joined England's coaching set-up under Roy Hodgson, Solskjaer does not see the double act being replicated off the field.
"Gary and Becks are two different personalities," he told Sportsweek.
"I'm sure Gary enjoys what he is doing but I'm not sure Becks is cut out for coaching. I can see him more on the other side of it."