"We are working diligently on multiple fronts to make this happen," said Ross Honey, senior director for media at Microsoft's content and partner strategy group. "The BBC is a great content provider."
It is not known whether UK gamers would pay for such services, however, as content is usually shown free to television licence payers, although the BBC does sell DVD box sets.
Honey said that Microsoft had also approached several other broadcasters in Europe.
Microsoft already runs a similar video-on-demand service for Xbox owners in the US, offering content from MTV, Disney, Fox, CBS, Paramount and Warner Bros.
The US service charges 160 Microsoft Points for a TV episode, 320 for a movie and 480 for an HD movie. 1,600 Microsoft Points costs US$19.99.
Television programmes purchased in the US can be kept indefinitely, while films have a lifespan of two weeks.
Microsoft also expects its console to be a big seller this Christmas, taking the top spot following its recent price cut.
Dan Cornelius, UK Xbox 360 marketing manager, said that the launch of the Elite version of the console and the price drops made the value-for-money gap between the Xbox 360 and Sony's PlayStation 3 much broader.
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