The cap space required to sign Jackson
As the Ravens placed the non-exclusive franchise tag on Jackson, he is due to earn $32.4 million this upcoming season as of right now. According to OverTheCap.com, the Atlanta Falcons currently have $66.4 million in cap space.
This is the largest amount of money the Falcons have had to spend in free agency in quite some time, and if they do trade for Jackson, they would be roughly spending half of their cap space on one player. One thing to note is that it is quite interesting that the Falcons went after Deshaun Watson despite all of the off-the-field problems/turmoil, but will now reportedly not be after Lamar Jackson (this brings about the idea that owner Arthur Blank spearheaded the campaign to acquire Watson, and now the decision to not go after Jackson is mutually shared by Fontenot and Smith).
While this isn’t a terrible idea given that Lamar Jackson is undeniably one of the best quarterbacks in the NFL, the Falcons have just recently gotten out of a dire situation regarding the cap. If they were to trade for Lamar and sign him to a new extension (this could lower his cap hit), that would presumably take up a large chunk of the cap space, leaving the Falcons with not as much money to improve the rest of the roster which is still several players away from seriously competing.
An argument could be made that adding Lamar Jackson would elevate the Falcons substantially; but given the way that Terry Fontenot works and the good situation with the cap space, it seems unlikely as the Falcons want to be shrewd in free agency and improve the roster in all aspects.