The team is scheduled to work out veteran guard Uche Nwaneri, who spent the preseason with the Dallas Cowboys.
Nwaneri started 92 games for the Jacksonville Jaguars from 2007 to '13.
Tight end Levine Toilolo, at 6-foot-8 and 265 pounds, had to line up at right tackle for the Falcons in place of Lamar Holmes to close out Sunday's 41-28 loss after Holmes, Hawley and Justin Blalock left the game with injuries.
Gabe Carimi finished at left guard for Blalock.
ESPN.com Falcons reporter Vaughn McClure contributed to this report.