Appearing on ESPN's SC6 (h/t Pro Football Talk's Michael David Smith), RG3 said the Arizona Cardinals and Baltimore Ravens each made him offers.
Griffin said he rejected the Cards since they had too many quarterbacks and he didn't believe he would get adequate practice time in a fourth-string role.
He also said the Ravens offered him a deal prior to their preseason opener against the Washington Redskins and wanted him to start the game, but he didn't think he would have enough preparation time.
Despite having missed the entire season to this point, Griffin is still hopeful a team will sign him, saying, "I love football. I miss the game. I am ready. So I haven't given up on 2017 yet. There are some teams that need help and may need help going into the playoffs."
The 27-year-old veteran played for the Cleveland Browns last season, but he was limited to just five games due to injury.
In those five games, Griffin threw for 886 yards, two touchdowns and three interceptions, while rushing for 190 yards and two scores. He also led Cleveland to its only win of the season.
On Wednesday, Griffin acknowledged he knew he was taking a risk by not accepting the offers made to him by Arizona and Baltimore: "I had interest in the offseason. It just wasn't the right fit and I had to make that decision for myself to say, 'Look, if I don't accept this offer, there's a chance I won't play football this year.' And I would talk to my family, and I was OK with that, OK with the fact that it might happen."
Griffin was once considered one of the NFL's fastest-rising stars after the Redskins selected him with the No. 2 overall pick in the 2012 NFL draft out of Baylor.
RG3 won Offensive Rookie of the Year honors in 2012, passing for 3,200 yards, 20 touchdowns and five interceptions to go along with 815 yards and seven scores on the ground.
Griffin was never the same after suffering a knee injury in a playoff loss to the Seattle Seahawks that season, however.
After posting a quarterback rating of 102.4 as a rookie, he never did better than 86.9 in four subsequent seasons.
He also relied far less on his legs after the injury, which made him a less dynamic player and easier for opposing defenses to account for.