Beckham joined Les Parisiens in January, notably donating his salary to charities in the city, though has had a rather indifferent campaign since joining the Ligue 1 leaders.
But reports over the weekend claimed that PSG were ready to offer the 38-year-old a one-year extension, and Ancelotti appeared open to the idea.
|11/8||PSG are 11/8 with BetVictor to beat Lyon on Sunday
While the former AC Milan and Chelsea boss expects Beckham to sign a new deal, he is less sure of his own future and has been continually quizzed over the identity of his whereabouts next term, but so far has refused to comment on any speculation involving his next move.
And speaking ahead of Sunday's match against Olympique Lyonnais, the coach maintained his coy stance, before putting to bed a rumour suggesting he had held talks with Manchester United about replacing Sir Alex Ferguson.
"About my future, there is no news. The season is not over yet. There are lots of rumours, but the club and I have agreed to speak at the end of the season. The appointment has been scheduled before next week," continued Ancelotti.
"That's absolutely not true [in response to claims that he was contacted by Manchester United]. [Sir Alex] Ferguson made a good choice with [David] Moyes. He has done a great job at Everton."
Les Parisiens can wrap up the Ligue 1 title with victory over Lyon on Sunday, and the former Chelsea boss admits the title race in France has "excited" him, while he is hopeful that Leonardo will not be sanctioned for his push on a match referee.
"To win a title in France is very exciting. It's exactly the same as any other trophy. I want to celebrate it with everyone. It is deserved," Ancelotti continued.
"Leonardo did not push the referee [against Valenciennes last weekend]. He is experienced and knows his football. I hope nothing will happen to him."