Keenum, 28,originally signed on with the Texans as an undrafted free agent out of Houston back in 2012. He lasted a few years with the Texans before he was waived at the start of the 2014 season and later claimed by the Rams.
Keenum later returned to the Texans at the end of the year, only to be traded back to the Rams for a 2016 seventh-round pick in March of last year.
The Rams used a first-round tender will cost them $3.635M million for the 2016 season.
According to OverTheCap.com, trading Keenum would free up $3,635,000 in available cap space while creating no dead money.
In 2015, Keenum appeared in six games for the Rams and completed 60.8 percent of his passes to go along with 828 yards, four touchdowns and one interception.