After Goldson worked out for the Falcons on Saturday, coach Dan Quinn made it clear the veteran safety would have to accept a backup role if he signs.
"We've been very clear about what we're looking for," general manager Thomas Dimitroff said. "[Goldson] knows what his role is going to be for us, and that's very important."
The Falcons will be without rookie starting strong safety Keanu Neal, their 2016 first-round pick, for at least the first two regular-season games with a right knee injury. Neal is scheduled to have arthroscopic surgery on Monday.
Backup safety? Kemal Ishmael will fill in for Neal, Quinn said. Ishmael has missed the past two preseason games with a shoulder injury, but he but could be back for Thursday night's final preseason game against the Jacksonville Jaguars?and should be ready for Week 1.
The Falcons need depth at strong safety, with unproven Damian Parms and Sharrod Neasman also on the 75-man roster behind Neal and Ishmael. The Falcons released veteran safety Sergio Brown on Saturday following a brief stint.
"I like the physicality," Quinn said of Goldson after his workout. "[Neal] is our guy, so we told Dashon that as well. And [Neal] will be back shortly. But [Goldson] did a really good job today, just moving around and his approach. You can really tell, even in a short interaction, what he stands for as a ballplayer."
Dimitroff echoed Quinn's thoughts on Goldson's physicality. ?
"Goldson looked good. He moved around well," Dimitroff said. "He came in at a solid weight. He's a big guy, as you know, who's rangy and can move around athletically for a guy who can play both strong and free [safety]. Obviously in our situation, he's more of a strong safety with this team."
Goldson started 15 regular-season games for the Redskins in 2015, as well as their playoff game against the Green Bay Packers. He finished with a career-best 110 tackles last season, his first with the Redskins.
Goldson has been fined a number of times in his career for illegal hits, including three times in 2013. He was suspended one game for a helmet-to-helmet hit early in the 2013 season, though it was later reduced to a $100,000 fine. Another hit drew a one-game suspension, costing him $264,705. After a third incident, he received a $60,000 fine. He did not receive a fine in 2015.
ESPN's Vaughn McClure and John Keim and The Associated Press contributed to this report.