He thought the interviews went well, hit it off with owner Arthur Blank and believed he was a perfect fit.
"Of all the places I went, I thought I had the best shot there in Atlanta," Ryan said. "I think I wanted that job more than I did maybe some other ones."
The feeling wasn't quite mutual, though, and the Falcons hired his friend and former colleague Mike Smith.
"I think I was too fat," Ryan said with a laugh.
He added that Baltimore was coming off a subpar season in which the Ravens went 5-11. It all worked out in the end for Ryan, in his first season as coach of the New York Jets (7-6) and looking to stay alive in the AFC playoff mix against Smith's Falcons (6-7).
"I think they made a great decision," Ryan said, grinning. "Not the best decision, but a great decision. No, but it's amazing how it works out. I'm certainly happy that it worked out like it did for both of us."
The two coached against each other at the college level - Ryan as the head coach at Morehead State and Smith at Tennessee Tech in the Ohio Valley Conference - and then worked together with the Ravens from 1999-2002.
"He's a great guy to hang out with," Smith said of Ryan. "When I say hang out with, it's in a social setting, because he has such a great personality. Everybody that has ever played for Rex Ryan will always tell you he's fun to play for and they always play hard."
The two talk throughout the season, and will share information if they face common opponents. This week is a little different, of course, with both teams needing victories to keep their playoff hopes going.
"We still have a chance," Falcons linebacker Curtis Lofton said. "We don't control our own destiny, but we still have a chance to make the playoffs, just like them."
The teams are going in opposite directions, though, and Atlanta is barely hanging on in the NFC postseason race. The Falcons have lost two straight and three of their last four, erasing the momentum of a 4-1 start.
"It's going to be a big game up there," Smith said. "They're fighting for their season, we're fighting for our season. There's three more games to be played. To me, it's going to be a good ballgame."
The Falcons face the prospect of playing without two of their best players on offense - quarterback Matt Ryan (turf toe) and running back Michael Turner (ankle) - for the third game in a row, although they returned to practice Thursday.
If Ryan can't go, Chris Redman will get his third straight start. Same for Jason Snelling, who has filled in adequately for Turner.
On top of that, they're dealing with some major off-field issues. Wide receiver and return specialist Eric Weems is facing a charge for driving under the influence, while defensive tackle Jonathan Babineaux is facing a felony marijuana possession charge following his arrest last week.
"We still have to go out and play a game," tight end Tony Gonzalez said. "We have to keep playing football."
That's what the Jets have done despite some key injuries of their own, including to quarterback Mark Sanchez. The rookie sprained the posterior cruciate ligament in his right knee on Dec. 3 and missed last week's game, but could return against the Falcons.
"I'm planning on it," Sanchez said earlier this week.
If Sanchez can't go, Kellen Clemens would start again for the Jets, who have won three straight since a horrific stretch during which they lost six of seven and appeared to have their playoff hopes dashed.
"Whether it be the mental mistakes, turnovers, we have done a lot of damage to ourselves," linebacker Calvin Pace said. "Now we're not beating ourselves. If we can keep that up, we'll be fine."
The Jets also need lots of help, though, with at least four teams ahead of them because of tiebreakers.
"If we don't beat Atlanta, then it doesn't really matter what happens the rest of the season," said running back Thomas Jones, fourth in the NFL with 1,167 yards rushing.
New York has the NFL's top-ranked overall defense and passing defense, led by shutdown cornerback Darrelle Revis, along with the league's No. 1 rushing offense. Those are numbers befitting of a conference leader, not a team on the outside of the playoff picture.
"They've got a lot to fight for," Falcons linebacker Mike Peterson said. "We've got a lot to play for as well."
If the Jets have one major advantage, it could be the weather. Forecasts call for a little snow and a high of 34 degrees, conditions that should favor the cold-weather New Yorkers.
"This is a dome team that's going to have to come into these elements," Rex Ryan said, "and face our fans, the weather, our team. It's going to be tough on them, that's for sure."
Oh, and Ryan had one more shot for his old friend: "Tell them to strap it up tight because it's going to be a physical game when they come here."
Smith laughed, expecting the trash talk from Ryan.
"That sounds just like Rex," he said. "And we will. I'm sure it will be a two-chinstrap game."