Goodell, who spoke with NFL Network's Alex Flanagan on Saturday during a sideline interview on NBC at the Western Michigan-Notre Dame game, doesn't plan to attend the meeting. Goodell said someone "from our staff" would meet with Favre.
NFL Network later said the meeting would be Tuesday in Minnesota with a member of the league's security team. An NFL spokesman declined further comment.
Goodell said Tuesday he had no plans to meet with Favre himself, but he added that it's something he would do if warranted.
"I haven't talked to anybody," Favre said. "I haven't declined."
NFL Network also said the league hadn't yet met with Jenn Sterger, the woman who allegedly received the messages and photos from Favre. Her manager declined comment.
Last week, the sports website Deadspin posted a video that contained the messages and voicemails, along with several below-the-waist photos -- said to be of Favre -- that were allegedly sent to Sterger's cell phone. Sterger, now a TV personality for the Versus network, didn't grant an interview to Deadspin for the report. The website said it bought the material from a third party it didn't identify.
Depending on what the league's investigation finds, Favre could be fined or suspended under the NFL's personal-conduct policy.
The Associated Press contributed to this report.