Dontari Poe is not an Atlanta Falcon, at least not yet.

Poe, the top free-agent nose tackle and formerly of the Kansas City Chiefs, visited the Falcons' facility on Tuesday but left without a contract. It was the third stop on Poe's free-agent trek following visits to Indianapolis and Jacksonville.

Now Poe is in Miami visiting the Dolphins, as ESPN's Josina Anderson reported. The fact that he hasn't secured a contract yet makes you wonder about his asking price. It also raises questions about his health, with reported concerns about Poe's back.

If it is all about the money, it would be surprising if the Falcons get into a bidding war, considering general manager Thomas Dimitroff already implied the Falcons wouldn't make a big splash in free agency. Sure, Poe could have a great impact on a defensive line in need of help, and his athleticism is off the charts for a guy who stands 6-foot-3 and weighs 346 pounds. But giving Poe, let's say, $10-$12 million in a one-year deal doesn't seem like the best option, even if another team is offering the same. His replacement in Kansas City, Bennie Logan, just received a one-year, $8 million deal that included $7.68 million guaranteed.

The Falcons don't have a ton of cap space. The latest NFLPA figures have them at around $14.5 million. Meanwhile, the Jaguars have $47 million in cap space, according to numbers obtained by ESPN's Field Yates.

Most cap space remaining, per official NFL accounting:

49ers: $73.9M

Browns: $61.4M

Jaguars: $47.0M

Titans: $42.3M

Raiders: $41.6M — Field Yates (@FieldYates) March 14, 2017

The other two teams on Poe's list -- the Colts and Dolphins -- have $37 million and $18 million in cap space, respectively, according to NFLPA figures.

We'll see how it all plays out from the Falcons' standpoint. They need to fill a hole at defensive tackle after cutting veteran Tyson Jackson and not re-signing veteran Jonathan Babineaux. They need a game-changing type player who can stop the run and has pass-rush ability. Poe has to the potential to be that guy, but will he consistently be that type of player? His production dropped the last two seasons after Pro Bowl showings in 2013 and 2014.

The Falcons have gone the bargain route with their other free-agent signings thus far, so maybe spending big on one wouldn't be all that bad. But again, it's hard to imagine the Falcons getting into a bidding war, especially against the cap-rich Jaguars.

Poe's willingness to accept a one-year deal seems to indicate the 26-year-old wants to prove himself and secure a lucrative, long-term deal after the 2017 season. Maybe the Falcons can convince him he'll have his best opportunity to shine playing for a team fresh off a Super Bowl. And maybe the Falcons can convince him to sign -- for the right price.