If the player reps endorse it, it would go to a vote of all players. If approved by players and then ratified by owners, the lockout would end, and a 72-game season would start Dec. 15.
A third option to be discussed is sending a counter-proposal back, sources told ESPN The Magazine senior writer Ric Bucher.
Taking a page from the owners' playbook, sources said the players union also could publicize details of the proposal and let NBA fans know that the 2011-12 season could be salvaged if the owners agree to it.
It's not certain what would comprise the players union's counter-proposal, but it's expected to be built off the owners' offer with a few changes.
But if the union leadership rejects the offer, the league is prepared to offer a harsher proposal -- one players wouldn't accept, possibly triggering a lengthy legal battle and certainly jeopardizing the 2011-12 season.
Some players were hoping for a say on the current proposal regardless of what the union's board does Monday.
"I think it's fair for every player to have a vote, because we're all grown men and its time for the players to control their career decisions, and not one player per team," Martin said in a text to ESPN.com's Henry Abbott. "If it comes down to a final decision, you got to be fair."
Commissioner David Stern has urged players to take the deal on the table, saying it's the best the NBA can offer and warned that decertification is not a winning strategy.
The current proposal calls for a 50-50 division of basketball-related income. Players are still unhappy with what they believe are too many restrictions for big-spending teams that would limit their free agent options, but Stern said the proposal is far better for players than the one player reps said they would reject last week.
Waiting is a proposal that calls for a 53-47 split of BRI in the owners' favor, a flex cap with a hard ceiling and rollbacks for current salaries.
Players could seek further tweaks to the current proposal before putting it to a vote, but Stern repeatedly has said the league is through negotiating.
"I want to answer this diplomatically. The next time we meet to discuss anything, we'll be discussing the 47 percent proposal," he told The Associated Press on Saturday. "This is it. We've been negotiating this for 2½ years. The owners authorized a revised proposal, and they said if it's not acceptable and they want to keep negotiating, we present them with a 47 percent, flex cap proposal. They know it."
Feedback from the players' union after a weekend of to examine the proposal wasn't positive, sources told Bucher.
The union's executive committee met for two hours Sunday night to examine the proposal.
One of the new wrinkles the committee has found difficult to accept, sources told Bucher, is an unlimited escrow system.
The escrow system would ensure that owners would be reimbursed for however much they exceed the negotiated amount of basketball-related income allowed to be spent on player salaries.
In the current seven-page proposal, a copy of which was obtained by ESPN The Magazine, the players have a choice of selecting a 50-50 split of BRI or a 49-51 band.
If teams spend more than the allotted percentage, they not only retain the 10 percent of each salary held in escrow, but if that 10 percent doesn't cover the excess then the additional funds can be deducted from a one percent of BRI dedicated to "post-career player annuity and player benefits."
If the excess still hasn't been satisfied, future benefits and escrow funds can be utilized to cover it. In essence, it assures the owners that no matter how much they spend in any one season, they will not have to pay more than the stated percentage.
Other elements in the deal that the union finds objectionable, a source said, are 12 percent reductions in both the minimum salary and the first-year salaries of first-round picks.
A league official said the proposal issued to media was a truncated version, and that the points left out were "B List" issues. Union sources say those issues were originally "B list" issues that the league elevated to vital parts of any new deal on Thursday.
Players also could vote to disband the union. Executive director Billy Hunter said last week he was aware that perhaps 200 players had signed a petition supporting it. But an antitrust lawsuit against the league would take months, so the best shot to play this season comes this week.
Stern reminded players and fans of that Sunday during an Internet blitz. He and deputy commissioner Adam Silver took questions on Twitter, and the league posted a memo on its website that Stern sent to players with a breakdown of various deal points. He urged players to "study our proposal carefully, and to accept it as a fair compromise of the issues between us."
The league has withdrawn its demands for a hard salary cap, salary rollbacks and non-guaranteed contracts during the negotiations. But players still fear some of the restrictions on teams over the luxury tax would act as a hard cap, which they vehemently oppose.
Stern has blamed agents for misinformation about the proposal that has spread since Thursday. So players were eager to get in the room with Hunter and union president Derek Fisher and get the full details themselves. Chris Duhon, Orlando's player rep, wrote on his Twitter feed that the Magic would accept the deal.
"The main thing is not going in with any preconceived notions," Minnesota Timberwolves rep Anthony Tolliver said. "We need to understand the ins and outs of the deal. It's just like last week, where we didn't understand the full extent of the deal until we got in the room face-to-face and talked it through."
Information from The Associated Press and ESPN The Magazine senior writer Ric Bucher was used in this report.