Alcon Entertainment, producers of the Blind Side and The Book of Eli, own the rights to make a prequel or sequel to Blade Runner. They seemingly haven't gotten much further than that. From Entertainment Weekly:
“We have some ideas that we’re not in a position to discuss yet,” Andrew Kosove, Alcon’s co-CEO, teases to EW. “But from our point of view, the thematic core of the original movie – what does it mean to be a human being? – is even more relevant today than it was when the film came out. After all, we’re living in the industrial age of technology.” Kosove and his fellow CEO, Broderick Johnson, are partnering on the project with Bud Yorkin, one of the producers of the original film. “That picture turned out so well – it’s just been selected for preservation by the Library of Congress – that for a long time I was afraid to try to make another one,” Yorkin says. “But now seems like the perfect time. We just need to find the right writer and director.”"New 'Blade Runner' producers talk movie prequel. Or maybe a sequel."