With Luck out of the picture, Jacoby Brissett will begin the 2019 season as the Colts' starting quarterback, while Phillip Walker and Chad Kelly are vying to be his backup.
The 28-year-old Osweiler spent last season with the Miami Dolphins. He appeared in seven games and made five starts, going 2-3. Overall, he completed 63.5 percent of his passes for 1,247 yards, six touchdowns and four interceptions.
Despite playing respectably when called upon last season, Osweiler went unsigned during the offseason.
Osweiler entered the NFL as a second-round pick in 2012, and he eventually became Peyton Manning's understudy. When Manning was struggling with injuries in 2015, Osweiler made seven starts and went 5-2.
He eventually lost the starting job back to Manning, and Manning helped lead Denver to a Super Bowl win. Manning retired after that, but Osweiler decided to sign with the Houston Texans rather than return to the Broncos and take over for Manning.
After he threw 15 touchdowns and 16 interceptions in his only season with the Texans in 2016, Osweiler returned to Denver as a backup in 2017 and then spent 2018 in Miami.
Osweiler has not shown that he can be a quality NFL quarterback over the long haul, but with a 15-15 career record as a starter and a touchdown-to-interception ration of 37:31, he apparently has done enough to earn a look in a backup capacity.
Since neither Walker nor Kelly have ever attempted a pass in a regular-season NFL game, there could be value in signing Osweiler to backup Brissett.
With Luck out for the season due to injury, Brissett started 15 games for the Colts in 2017. He went 4-11 and completed 58.8 percent of his passes for 3,098 yards, 13 touchdowns and seven interceptions, while also rushing for four scores.
It is difficult to say if Brissett has what it takes to be the long-term answer at quarterback for Indianapolis, and that uncertainty creates even more of a need for an experienced option behind him.