Milan are desperate to keep the 33-year-old England midfielder, who set up two goals in Sunday's 3-0 win at Lazio, but Galaxy have said he must return in March.
"We have included him because he is playing well," Ancelotti told Sky.
"Of course I've said before I'm happy to be playing here," he told reporters. "It's a great club with great players and now we are in a good position. I'm taking each game as it comes and enjoying it."
Beckham joined Milan to stay in the England reckoning during the long U.S. close season and he is now hopeful of a place in Fabio Capello's squad for the February 11 friendly in Spain.
"The manager has said it about every player, if players are playing well and are fit they've got a chance of being in the squad. That's all I can do," he added. "I hope I get picked, if not I'll carry on enjoying my football here and work hard."
Long-term injury victims Alessandro Nesta and Gennaro Gattuso are also on Milan's new UEFA Cup list which teams cannot add to for the remainder of the season.
