"We're just looking for facts now," Goodell said at the NFL Fall League Meeting. "I am going to deal with it as we get the facts."
Goodell said he didn't have plans to meet with Favre, "but if it is something that would help us get to a conclusion and it is warranted, I will do so."
The investigation, announced last week, centers on a report by the sports website Deadspin that Favre, then with the Jets, sent the photos and messages to Jenn Sterger in 2008.
Sterger's manager, Phil Reese, declined to say if his client has talked with the NFL.
"This is something that allegedly happened two years ago," Reese said in an e-mail to The Associated Press. "We don't want a quick resolution, but the proper resolution."
Favre could be fined or suspended under the NFL's personal-conduct policy.
"One of the reasons we instituted the personal-conduct policy ... to make everyone understand their responsibilities," Goodell said. "We're not going down a line of speculation and hypothetical situations."
Favre hasn't responded to questions about the Deadspin report.
Two high-profile quarterbacks recently were penalized for violating the NFL's personal-conduct policy.
Pittsburgh Steelers quarterback Ben Roethlisberger was suspended for six games in April after he was accused of, but not charged with, sexually assaulting a 20-year-old woman at a bar in a Georgia college town. Goodell shortened that ban to four games just before the season, and Roethlisberger will return to the field for Sunday's game against the Cleveland Browns.
Copyright 2010 by The Associated Press