Goodell said National Football League officials would probably be too busy with the three-day player draft starting on Thursday night in New York to wrap up a decision on punishment for players who were rewarded for injuring opponents.
"We're in the final stages of working on the discipline involving the player and we hope to be done very soon to get that behind us," Goodell told reporters at an NFL draft event.
"We want to complete the work that we've started to make sure we're thorough and fair. I would think that with all we have to do on the draft for the next couple of days, it's not likely."
The NFL is still doing interviews regarding a program used by the Saints from 2009 to 2011 that has already led to heavy punishment for the franchise, including a season-long suspension for head coach Sean Payton, eight games for general manger Mickey Loomis and six games for assistant Joey Vitt.
"Once we're done, we'll issue it."
According to Goodell, the NFL is also following a federal investigation into whether Loomis had his home team's stadium wired so that he could listen in on opposing team's coaches. The Saints have denied the allegations.
"As I understand it, it's been given to federal authorities," Goodell said about the latest controversy to hit the Saints, which was first reported by an ESPN investigative program.
"They are doing their work. We are waiting and we'll see if there's any credible information that comes from that and at that point in time, we'll take whatever steps are necessary, if necessary."