The anticipated move comes in response to injuries to Houston Texans quarterbacks Ryan Fitzpatrick and Tom Savage on Sunday.
After Mallett was forced out of the lineup by a pectoral injury following the team's Nov. 23 loss to the Bengals, Fitzpatrick again took over the starting role.
In Sunday's loss to the Indianapolis Colts, Fitzpatrick sustained a broken leg and was replaced by rookie quarterback Tom Savage. Savage, however, was hit in the knees on the game's second-to-last play and limped off the field.
The Houston Chronicle reported on Sunday afternoon that Savage, who went 10-of-19 for 127 yards and an interception against the Colts, would undergo an MRI.
Keenum joined the Texans in 2012 as a free agent. He started eight games in 2013, completing 54 percent of his passes for 1,760 yards, nine touchdowns and six interceptions.
Depending on the severity of Savage's injury, Keenum may be one of two quarterbacks Houston adds to the roster, according to the report.
Keenum spent the offseason working with coach Bill O'Brien and QB coach George Godsey, so he knows a lot about the system.— John McClain (@McClain_on_NFL) December 15, 2014
Keenum will join Thad Lewis and perhaps another QB on the roster if Tom Savage's knee injury is as serious as some believe it is.— John McClain (@McClain_on_NFL) December 15, 2014
The Texans are 7-7 so far this season and currently are second to Indianapolis in the AFC South. They host the Baltimore Ravens (9-5) next Sunday.