The idea is part of director of television Jana Bennett's TV Plus project - a new media pilot running until Christmas.
The corporation is already trialling three clips from BBC3 sitcom Nighty Nighton mobile phones to see what kind of scenes work best on the format. It will then use this knowledge to ask writers to think of mobile phone-friendly sketches.
Clear scenes with basic punchlines - such as slapstick routines - are believed to be better suited to phones than complicated scenes with lots of dialogue. Back stories could also be shot exclusively for the web.
"At the moment we're going through already shot footage," said Bennett. "We want to get to the next level, where we're actually commissioning specifically for that format, and commissioning from scratch."
The corporation is currently searching for an idea that it thinks is suitable for the scheme and wants to get the project started before Christmas.
The extra content will be used as viral marketing to promote the series before it goes on air, as well as showcasing mobile phones' potential.
"We all know of schoolkids swapping clips on the bus. Do we specifically tailor slapstick and catchphrases to mobile phones?" said Bennett.
Interactive features around the new Doctor Whoseries are being developed for mobiles, the internet and red button services, aimed at marketing the programme before the second series goes on air.