After more than a year of fighting and litigation over how the NFL investigates and metes out punishment to its players, league officials and the union are moving closer to a deal that would involve Commissioner Roger Goodell giving up power over off-the-field player discipline, NFL Players Association executive director DeMaurice Smith said Monday.

No deal has been reached, significant obstacles remain, and any potential deal will not happen soon, people involved with the matter said. However, Smith said he remains optimistic...