Tom Pelissero

USA TODAY Sports

The NFL Players Association is expecting another proposal from the league Tuesday morning on a new drug policy that could go to a vote among player representatives as soon as Tuesday night, a person with knowledge of the negotiations told USA TODAY Sports.

The sides met for 3 hours Monday in New York, and players presented the parameters of what they'd accept on the outstanding issues, said the person, who spoke on condition of anonymity because they weren't authorized to discuss the talks publicly.

The expectation is the league will file the next proposal by noon Tuesday, the person said, giving the union's legal team time to review it before presenting it to the reps on a conference call before a vote.

The sides have been exchanging proposals the past month in hopes of getting a deal done before the season began last week. They agreed more than a year ago to procedures on testing for human growth hormone as promised in the 2011 collective bargaining agreement.

But talks got hung up last week on issues related to marijuana, the league's desire to punish league personnel upon a DUI arrest before due process and what to do with suspended players such as Wes Welker and Josh Gordon whose cases might change under the new policy.

If a deal were approved Tuesday night, any players whose suspensions are reversed would have time to prepare to play in Week 2. But it remains to be seen exactly what is, and isn't, in the league's proposal.