For those not familiar with them, these short stories (each about 100 pages long) commence eighty-nine years before the events of Game of Thrones and depict the life stories of Aegon V Targaryen and the hedge knight Ser Duncan the Tall (mentioned in a Season 1 episode by Old Nan), and their lifelong friendship which begins at a tourney at Ashford. Martin has said that he has plans to write anything from nine to twelve of these stories. The novel A Storm of Swords features a section where Ser Jaime Lannister reads up on Dunk's life story, hinting that their stories will end on the night of the great fire of Summerhall on the night Prince Rhaegar Targaryen was born. This suggests that the Dunk and Egg stories will span a period of almost exactly fifty years.
Whether HBO are considering a TV movie, a theatrical adaptation or a full spin-off series is uncertain. I think a spin-off series is more likely. This would be a much more episodic series than Game of Thrones, with more of an 'adventure of the week' feel. That said, there would be some over-arcing storylines, as there are in the short stories, particularly those related to the doings of the King's Hand, Lord Brynden Rivers, popularly known as 'Bloodraven' (he's also mentioned a few times in the books). Characters such as Walder Frey and Maester Aemon also show up in the D&E stories, the former as a four-year-old child and the latter as a young man studying at the Citadel in Oldtown. It would be interesting if a proposed TV series also followed the format of the short stories, with years falling between each adventure and the whole thing spanning a period of five decades (which would presumably necessitate recasting Egg - who starts the series as a ten-year-old - at some point).
In the same linked article, Martin also confirms that he will be proposing a TV series based on his novel/short story collection Tuf Voyaging, in the near future. Tuf Voyaging is a space opera, set in Martin's Thousand Worlds SF setting, and focuses on the adventures of Haviland Tuf, the commander of an ecological preservation starship and its enormous collection of species (human and alien) it is seeding on various worlds across the galaxy. Martin also reveals that vampire novel Fevre Dream is in development as a film (with possible interest from a 'name' director) and that progress is being made on the Wild Cards movie, which will be a co-production between SyFy and Universal.