The ex-Jaguars QB will sit down with the Rams on Monday according to NFL.com.
Bortles, who was the third overall pick in the 2014 NFL Draft by the Jaguars, was released by Jacksonville on Wednesday as they announced the signing of new starting quarterback Nick Foles.
The Rams already have a starter at quarterback in Jared Goff, but could bring in Bortles to be the teams' new backup quarterback, as 2018 backup Sean Mannion is currently a free agent.
During his time in Jacksonville, Bortles went 24-49 as a starter, going 3-9 last season, a year after leading the Jaguars to the AFC Championship Game, which they lost to the New England Patriots.
Last season, Bortles threw for 2,718 yards, with 13 touchdowns and 11 interceptions with a quarterback rating of 44.1.
In five seasons, Bortles has thrown for 17,646 yards with 103 touchdowns and 75 interceptions with a quarterback rating of 80.6.
In 2018, Goff started all 16 games for the NFC champions, throwing all but seven passes for the team overall.