Stern said that Johnson will attend an April 17-18 owners meeting in New York to deliver his proposal, but the league expects to have heard it by then.
"We have an April 17th meeting of the board, but if the mayor follows through on what he's told us, we'll have it comfortably by March 1," Stern said Thursday.
Johnson is trying to line up investors to buy the Kings and keep them in his city with a new arena, rather than watch them move to Seattle.
Speaking at an All-Star weekend event, Stern also said he doesn't currently see "a push for expansion" among owners, knocking down the idea that both cities could end up with teams.
"My statement about expansion is talk to Adam next year," Stern said, with commissioner-elect Adam Silver standing behind him. "I don't have any plans to champion expansion between now and Feb. 1, 2014. That's up to the ownership and the commissioner."
Stern will retire as commissioner on that date.
A Seattle group led by Chris Hansen and Steve Ballmer has reached an agreement with the Maloof family to buy 65 percent of the franchise, which is valued at $525 million, and move the team to Seattle and restore the SuperSonics name. The deal will cost the Hansen group a little more than $340 million.
Johnson has since vowed to put together a "fair and competitive offer" to keep the team in California's capital city, with a plan to help finance a new downtown arena.
The mayor has introduced more than 20 local investors who have pledged at least $1 million each to be minority owners in the team, but he has yet to announce the major equity partners.
Stern said he has no meetings scheduled this weekend with Johnson, who plans to be in Houston, but said the former NBA All-Star may even meet with the board before April.
Until then, the Seattle group will have to wait.
"We have a process that we've been doing for the last some-odd years, probably 50, where we take applications, we do all the work and the work has begun," Stern said. "And so the April 18th board meeting is what we're aiming for for final resolution on this issue."
Stern spoke after joining former NBA star Bob Lanier, a special assistant to the commissioner, to announce a four-year contract extension between the league and the Retired Players Association, commemorating their 20-year partnership.