NFL head coaches don't often have long shelf lives. The moment you begin to think it's okay to get comfortable, the team hits a rough stretch - or two or three or four - and the rumors about your all-but-certain demise begin to circulate.

One such coach, the Atlanta Falcons' Mike Smith, has had his name bandied about in recent days as his obviously flawed team fights to stay relevant.

If he were fired - and many in and around the league suspect he could be dismissed if the team underperforms again this season - could the New York Jets head coach Rex Ryan - also not yet fired but certain to be staring at a very open calendar come the offseason - be a good bet to take over?

According to Jason Cole of Bleacherreport.com, people within the league view the two as a "natural" fit and suspect that Ryan will be a top candidate should circumstances ultimately prove favorable.

"Couple of sources reiterated today that Rex Ryan to #Falcons seems natural considering need to upgrade D & that he interviewed there in 2008," Cole tweeted.

The team would of course need to make a final determination on their current head coach first.

Smith, while he found great success initially and has continued to find great regular season success, has seen his team annually falter in the season's biggest moments. From 2010 to 2012, they finished either first or second in the NFC South, but failed to advance to the Super Bowl, losing in the Divisional game, the Wild-Card game and the NFC Championship game, respectively.

Last season, they managed only four victories and missed the playoffs entirely.

This year, Smith's Falcons are 5-9 and both on the verge of another postseason-less year and still very much alive, thanks to the dumpster fire that is their division. If they do miss the playoffs, could it be the final straw that pushes owner Arthur Blank to remove Smith and replace him with a coach like Sexy Rexy?

For his own part, Ryan, always known for his defensive acumen, recently lamented to George Willis of the New York Post that what has ultimately doomed his team this season, and seemingly his tenure with the organization, is stability, or a lack thereof, at quarterback.

"Brady is a huge reason for it," Ryan said, choosing his words wisely, but still sounding altogether wistful and longing while comparing his downtrodden Jets to the perennially successful New England Patriots. "It's obviously a very successful system. But I think having that consistency at the quarterback position probably makes it a little easier than maybe other teams have gone through. I'll just leave it at that."

Guess what team has an extremely stable QB position, a defense direly requiring a fresh scheme and personnel overhaul and the potential need for a new coach?

The Atlanta Falcons.