The videos show a woman displaying her toes to an off-screen cameraman who, in one video, sounds a lot like the coach. The two are having an intimate chat about her feet.
During his news conference Wednesday, Ryan declined several times to discuss the situation.
"I understand I'm going to get asked this question frontways, sideways, backways, and all this, but it is a personal matter," he said.
When asked if the NFL might look into the situation, spokesman Greg Aiello said the league considers it "a personal matter."
Jets general manager Mike Tannenbaum said in a brief statement that he and owner Woody Johnson have met with Ryan. They also are calling it a personal matter, adding that the coach has their "full support."
The NFL is still investigating those allegations.
According to Deadspin, the woman in the video goes by the handle "ihaveprettyfeet."
A still photograph from one of the video clips was splashed across the front of the New York Daily News and showed a woman with her feet hanging out of an SUV. She is approached by someone who isn't on camera, and he tells her that she has "really beautiful feet."
The other videos show the woman sitting on a couch, having a drink, reading a book and sitting on a porch and rubbing her feet.
"My wife's beautiful," Ryan said Wednesday when asked about his wife. "We've been married for 23 years. She's awesome."
"I don't want to say that I probably shouldn't have done that," Ryan said.
"I'm going to be ready to play Chicago," Ryan said. "We're going to be ready to play Chicago. I am ready. This is my job, and I'm focused on the job at hand."
Most players also declined comment on the issue, but All-Pro cornerback Darrelle Revis supported his coach.
"You hear stuff around the building and whatever it was, I haven't even seen the video, you hear stuff," Revis said. "Foot fetish? Whatever. I mean, that's his wife. At the end of the day, that's his wife, and he can do whatever he wants with his wife. It's not like he's out committing adultery or anything negative."
Sal Alosi, the Jets' strength and conditioning coach, was suspended without pay for the rest of the season, including the playoffs, and fined an additional $25,000.
In January, Ryan was fined $50,000 by the team after he was caught on a cell-phone camera flipping his middle finger at a fan during a mixed martial arts competition in Sunrise, Fla. The image of Ryan quickly spread across the Internet and made its way onto the back pages of New York tabloids. He apologized the next day in a statement, calling his actions "stupid and inappropriate."
Copyright 2010 by The Associated Press