Per USA Today's Kevin Allen and Tom Schad, AAF chairman Tom Dundon said the league has been in contact with Manziel's camp about potentially working out for teams.
"Right now, it's a decision of the GMs, and they can decide what they want to do," Dundon said. "If talent-wise this is close, the negative of him is that there is drama with him and you are trying to win games and build a team. The positive is that he brings in fans and attention."
The Alouettes announced Wednesday Manziel was being released after "it was found he had contravened the agreement" with the CFL that made him eligible to play.
After news of Manziel's release broke, the former Heisman Trophy winner tweeted his thanks to the Montreal organization and said he was looking "forward to exploring new options within the United States."
Dundon noted Manziel hasn't indicated he will take a workout with the league, but in the event he is offered a contract from the AAF, it would be the same three-year, $250,000 deal every player in the league receives.
Three weeks into its inaugural season, the AAF has already experienced financial difficulties. The Athletic's David Glenn reported Dundon, who also owns the Carolina Hurricanes, made a $250 million investment in the league to take over as chairman and help make payroll.
Manziel appeared in eight games for Montreal during the 2018 season. He had five touchdowns, seven interceptions and 1,290 passing yards.
It was Manziel's first game action since he was released by the Cleveland Browns in March 2016. The 26-year-old was charged with assault against his ex-girlfriend but it was later dismissed in November 2017.