The vastly-experienced manager is just one of a number of managers being tipped to replace Guus Hiddink at Chelsea at the end of the current season.
Russia coach Hiddink has been entrusted with first-team affairs at Stamford Bridge following Luiz Felipe Scolari's sacking.
Beckham, who is currently on loan at Milan from Los Angeles Galaxy, however, cannot confirm whether Ancelotti could be Chelsea-bound.
English"When I arrived at Milan, Ancelotti was already studying English," explained Beckham.
"Every time I try to fix his English, he insists on making errors and we end up laughing.
"I can't tell you anything about Chelsea."
Meanwhile, Beckham has confirmed he has not made significant inroads regarding his Italian, although he has no regrets about prolonging his Serie A stay using his own money.
Little progress"I admit I haven't made much progress with Italian. I can only say 'congratulations' to the referee or 'good goal' to Pippo Inzaghi," he continued.
"Paolo Maldini speaks English and there is also Gennaro Gattuso, who speaks a language of his own, but I understand him perfectly.
"One thing is for sure - there are many players in Europe and the world that would pay out of their own pocket to play at a club like Milan.
"So I would have done anything to stay here until the end of the season."
It has emerged that the MLS will receive $10million (£6.8m) for agreeing to extend Beckham's loan through to the end of the current campaign.