The league wrote a letter to the NFLPA, offering to work with them to study the potential use by players as a pain management tool, the source confirmed.
The letter was first reported Tuesday by the Washington Post. The NFLPA has not yet responded to the offer, and did not immediately respond to the Post for comment. It is conducting its own study.
"We look forward to working with the players' association on all issues involving the health and safety of our players," said Joe Lockhart, the NFL's executive vice president of communications.
The NFL's letter pointed out a few areas for potential research, including pain management for acute and chronic conditions. The league has previously indicated that it is studying marijuana as a pain management tool on its own.
NFLPA executive director DeMaurice Smith told the Washington Post in January that the union was working on a proposal on a "less punitive" approach to recreational marijuana use.
"I do think that issues of addressing it more in a treatment and less punitive measure is appropriate," Smith said at the time. "I think it's important to look at whether there are addiction issues. And I think it's important to not simply assume recreation is the reason it's being used."
Players are currently tested for marijuana and face potential discipline for positive tests.