The NBA's relocation committee will have a conference call next Monday to discuss the Kings sale, at which point a recommendation is expected to be made, according to TNT's David Aldridge (via Twitter). That recommendation would be taken to the NBA's Board of Governors, who would then vote on the fate of the Kings (Twitter link).
Aldridge suggests that if the process continues on schedule, a final vote on the Kings could happen as early as May 8th, though Chris Daniels of KING TV in Seattle believes a vote during the week of May 13th may be more likely (Twitter link). As Daniels notes, the situation remains fluid, having been delayed already, but commissioner David Stern has said there will be resolution in time for May 21st's draft lottery.
The NBA's finance and relocation committees are made up of a handful of NBA owners, who will in turn make their recommendation to all 30 owners on whether or not to approve the sale and relocation of the Kings.