According to NFL Network's Mike Garafolo, Finley will serve as Allen's backup despite the fact that Allen was just called up from the practice squad.
Rookie No. 1 overall pick Joe Burrow suffered a season-ending knee injury in last week's loss to the Washington Football Team, forcing Bengals head coach Zac Taylor to weigh his other options under center.
Although the Bengals are just 2-7-1 this season, Burrow made a strong impression and gave every indication that he is Cincinnati's long-term answer at quarterback.
He was firmly in the Offensive Rookie of the Year conversation prior to the injury, completing 65.3 percent of his passes for 2,688 yards, 13 touchdowns and five interceptions and recording three rushing touchdowns.
Replacing that production will likely be impossible for the Bengals for the remainder of the season.
The 28-year-old Allen, who was a sixth-round pick of the Jacksonville Jaguars in the the 2016 NFL draft out of Arkansas, saw his first regular-season game action last season with the Denver Broncos.
He started three games in place of the injured Drew Lock, going 1-2 and completing 46.4 percent of his passes for 515 yards with three touchdowns and two picks.
That level of production doesn't necessarily inspire much confidence, but the same can be said for Finley, who was the Bengals' fourth-round pick last year out of NC State.
Taylor gave Finley three starts last season in place of veteran Andy Dalton, and the results weren't great, as he went 0-3 while completing 47.1 percent of his passes for 474 yards with two touchdowns and two interceptions.
Finley played so poorly that Taylor went back to Dalton despite knowing Dalton likely wasn't part of the team's long-term plans.
After Burrow left last week's game because of his knee injury, Finley stepped in and struggled mightily, going 3-of-10 for 30 yards with no touchdowns and one pick.
There clearly isn't an ideal option at quarterback on Cincinnati's roster, but Taylor apparently hopes Allen can better utilize weapons such as Tyler Boyd, Tee Higgins and A.J. Green than Finley has thus far in his young career.