The league told the union that it was free to question any current or former Saints officials about the matter, but that it would not delay announcing its own discipline. That announcement is expected to come soon.
Union officials contend they didn't learn of the investigation until shortly before the results were announced, at which point they told the league they wanted to conduct their own investigation.
"We have given your requests careful consideration, and have concluded that there is no basis for delaying the imposition of any discipline in this matter, and particularly not as it may apply to a club or any non-player employee of a club," NFL attorney Jeff Pash wrote in the letter to union general counsel Richard Berthelsen on Wednesday. "Any disciplinary action affecting any player would be imposed only in a manner consistent with our Collective Bargaining Agreement. As you know, the sole authority to investigate and impose discipline in this matter rests with the Commissioner."
Pash also wrote that team officials were free to speak with union investigators, but that the league "will neither compel them to do so, nor direct them to refrain from doing so."
The NFL says the Saints ran a program that gave thousands of dollars in payoffs to players for hits that knocked opponents out of games. The NFL said the amounts reached their peak in 2009, the season the Saints won the Super Bowl. Former Saints assistant coach Gregg Williams, now defensive coordinator of the Rams, has admitted to and apologized for running the program.
The Associated Press contributed to this story.