Bryan Cogman, Executive Story Editor/Writer.
George R.R. Martin has confirmed that he's worked with Cogman on developing some ideas for the spin-off. Intriguingly, Martin has said that Cogman's project will be an "adaptation", in contrast to the other four series which are all original ideas.
Martin has previously ruled out a series based on Robert's Rebellion, saying it would just be "joining the dots" and all the major plot revelations from the war will be revealed in the books or TV series. He has also ruled out a series based on the Dunk & Egg prequel novellas, since he has only written three of a possible twelve (maximum) stories in the series and wants more in print before he commits to a TV deal.
On the surface this really only leaves one potential other possibility: a TV series based on the Dance of Dragons and the lead-up to it, previously explored in Martin's short stories The Princess and the Queen and The Rogue Prince. This story has several possibilities for drama: it tells the story of the deaths of the original Targaryen dragons and the near-ruin of the house. It features a major civil war and political scheming, and several exciting and unpredictable plot twists. There are heroes and villains on both sides of the war, as well as huge battles and several major dragon-on-dragon fights (which would be something different from Game of Thrones itself). Although the budgetary considerations would be daunting, Season 7 of Game of Thrones shows that HBO are willing to spend big to get big results. If they use The Rogue Prince as the basis of the start of the story, they could also start quite small and then build up to the start of the war over one or two seasons to gauge interest before committing the big bucks.
It is also possible that Martin has given Cogman are sneak-peek at The Sons of the Dragon, the novella about Aegon the Conqueror's sons Aenys and Maegor that will appear in next month's Book of Swords anthology. Of course, if GRRM is using the term quite loosely, then an "adaptation" could apply to almost any story or episode from The World of Ice and Fire or the upcoming Fire and Blood, Volume I, which expands the potential sources for the story quite widely.
HBO continue to develop the five projects and will likely select one or two to move to the pilot stage next year. HBO hopes to have a show ready to go within a year or two of Game of Thrones concluding in late 2018 or early 2019.