Investigators still have "some additional work" to do, Goodell told reporters at a "Play 60'' youth football event at New York's Chelsea Waterside Park, USA Today reported.
"We should be in a position where we should be able to wrap that up soon and as soon as we do, we'll let you know our decision. ... We expect to be doing that very soon to get that behind us. …
"In my office I have an NFL shield up and I point to that and said, 'Everything we do has to reflect well on the integrity of the league and that shield,'' Goodell said. "And everything that they do and I do, our clubs, coaches do has to reflect well on that.
"And it's our responsibility to improve the integrity of the league and make the league better than when they came into it. I think they all understood that.''
Former Saints defensive coordinator Gregg Williams was suspended indefinitely for his lead role in "Bountygate," a 2009-11 program that paid bonuses to players who intentionally injured opponents.
New Orleans Coach Sean Payton was suspended for the 2012 season and General Manager Mickey Loomis was suspended for eight regular-season games.
Penalties for players involved in the bounty program likely would not be announced before the NFL draft, which begins Thursday, the newspaper said.
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