The NFL and the NFL Players Association are making progress toward an agreement on revisions to the player-disciplinary system that likely would change Commissioner Roger Goodell’s role in the appeals process, according to people familiar with the deliberations.

An accord appears within reach as the negotiations continue. But the timetable for completing a deal is unclear and if those close to the process know at this point what Goodell’s modified role will be, they’re not saying.

According to one person with knowledge of the proceedings, “slow progress” is being made in the talks. That person expressed doubt that a deal will be struck soon but added that the two sides probably “will get there eventually.”

Others connected to the process expressed similar sentiments, saying the negotiations are ongoing and moving toward a compromise but it’s not clear when a resolution might be reached.

The NFLPA is seeking neutral arbitration for appeals by players of discipline imposed by the league under the sport’s personal conduct policy and integrity-of-the-game rules. Currently such appeals are heard and resolved by Goodell or a person appointed by him.

The union has made successful courtroom challenges of discipline imposed by the league on Adrian Peterson under the personal conduct policy and Tom Brady under the integrity-of-the-game rules. The NFLPA also points to running back Ray Rice’s suspension being overturned on appeal when Goodell appointed a former federal judge, Barbara S. Jones, to resolve that case.

Goodell has said he is willing to consider changes to the system of player discipline but is not willing to surrender his authority to resolve appeals to a third-party arbitrator.

DeMaurice Smith, the executive director of the NFL Players Association, said in November that the league and union are having “the right conversations” toward a possible agreement on the issue. He said during Super Bowl week he was hopeful a deal would be struck.

“We have had a number of conversations and those conversations are ongoing,” Smith said three days before the Super Bowl. “I’m cautiously optimistic that we can reach a resolution on a number of those issues. And I think sort of the frame continues to be the same. We believe that a collectively bargained change to the system is good for everyone.”

Goodell said the following day at his annual state-of-the-league address: “We’ll continue the dialogue. If we can find changes, if we can improve that process, we will do that.”

Players already have third-party arbitration for appeals of discipline under the sport’s drug policies and for illegal on-field hits.

The issue is about to become prominent again with the league’s appeal of the federal judge’s ruling that overturned the NFL’s four-game suspension of Brady, the four-time Super Bowl-winning quarterback for the New England Patriots, in the DeflateGate controversy.

The U.S. Court of Appeals for the Second Circuit is scheduled to hear the NFL’s appeal March 3. Goodell declined to say at the Super Bowl whether the league would reinstate Brady’s suspension if it prevails in the federal appeals court.

Eric Winston, the Cincinnati Bengals offensive tackle who is the union’s president, said at the Super Bowl it remained to be seen what the middle ground might be on the NFLPA’s insistence on third-party appeals and Goodell’s resistance to that.

“We’ll see,” Winston said then. “I guess at the end of the day that’s where the compromise comes from. We’ll see what happens. Obviously it seems very straightforward. But when you get into the idea of when you start talking about the initial investigation, when you start talking about the initial punishment to the appeal, there’s a lot of layers of the onion to peel back there.

“And so as we know in collective bargaining, you’re not going to get everything you want. But I think both parties understand that there’s some issues to be fixed and hopefully we can get to a point where it’s official and we actually end the thing.”