Rooney, a lifelong Republican, was picked by President Barack Obama earlier this year to be U.S. ambassador to Ireland.
"When he gets concluded with his tutoring, I will probably speak with him and we'll make a determination from there," Goodell said.
The Rooney Rule was born nearly seven years ago, when two lawyers threatened to sue the NFL if it didn't open up more opportunities for minorities. Rooney led a committee to develop a policy to stop what the league viewed as an embarrassing lack of diversity.
Expanding that policy to GMs isn't expected to meet much resistance.
"It's a good idea," Dolphins owner Stephen Ross said. "We certainly have it with the coaches and this would be expanding it to the general managers. From what I understand, we did follow that when we did hire Bill Parcells."
In other developments before the meetings closed Wednesday morning with a 2 1/2-hour session:
-Seeking ways to generate new revenue streams, NFL clubs can now arrange to have their logos on cards sold by their respective state lotteries.
Delaware became the only state east of the Mississippi River to allow betting on sports after new legislation was signed last week. The NFL is strongly against betting on the outcome of games, but said the lottery move could generate significant money to be directed back to "many different public purposes," Goodell said.
In states where there are more than one NFL team, those clubs will be expected to negotiate how to proceed with the lottery.
-Talks were held on a tougher anti-tampering stance involving free agents, although Goodell said some owners simply suggested that clubs adhere to the rules already in place.
Some teams have said clubs have illegally reached out to agents before signing periods begin, which could theoretically make it tougher for a team to re-sign its own player. The proposed change would likely install a short window of opportunity for teams to talk to free agents before the signing period begins - but with no contracts finalized.
"We're discussing it, that's all," Atlanta Falcons owner Arthur Blank said.
The issue was tabled Wednesday. Talks will continue, Goodell said, and a vote is likely in October.
Notes: More talks were held on a 17- or 18-game regular season, but once again no vote was held and the league's analysis of such a move will continue. We did not take any action, but it was a very good discussion," Goodell said.