The Colts currently have two other quarterbacks on their roster in Phillip Walker and Chad Kelly. Walker has never played in a regular-season game, and Kelly is serving a two-game suspension for a violation of the NFL's personal conduct policy.
"Those are all really good things to consider that we are considering very strongly," Reich said Monday. "Phil [Walker] has been here for a while so we have a lot of belief and confidence in Phillip. He knows our offense. He knows this locker room. Those are going to be the decisions that we have to make in the next week to 10 days."
Osweiler, 28, posted a 2-3 record with the Miami Dolphins last season while filling in for the injured Ryan Tannehill. He completed 63.5 percent of his passes for 1,247 yards, six touchdowns and four interceptions in 2018.
The Denver Broncos selected Osweiler in the second round of the 2012 NFL Draft out of Arizona State. He is entering his seventh season in the league.