The league is looking into the matter under its personal conduct policy.
"We are going through that and we are making sure we understand all the facts," Goodell said at halftime of the Chargers-Raiders game.
Goodell added once the investigation is complete, "we'll make a determination from there."
Should Favre be found to have violated the NFL's conduct policy, he could be fined or suspended.
Deadspin posted a story Thursday which included several voicemails allegedly sent by Favre to Jenn Sterger, who worked for the Jets at the time. The voicemails include a man asking to meet with Sterger, who now is a TV personality for the Versus network. The website posted a video that contained the voicemails and several graphic pictures - said to be Favre - that were allegedly sent to Sterger's cell phone.
The website later reported that Favre also pursued two female massage therapists who worked part time for the team, according to one of the women. Deadspin did not identify the women, but a Jets spokesman said the team was giving contact information for the two women to the league.
Sterger's manager, Phil Reese, has said his client "did not provide Deadspin with any information." And a Deadspin editor said it paid a third party for the material and acknowledged it's possible the man who sent the voicemails and photos may not be Favre.
Favre refused to comment on the stories earlier in the week. Minnesota is at the Jets on Monday night.
Vikings coach Brad Childress said he talked with Favre about the NFL investigation and that the Deadspin reports have not been a distraction for the team .
"We just talk about what's out there and look it right in the eye and deal with it to the extent we can," Childress said on Saturday. "It doesn't affect anybody else in this locker room, except Brett Favre."