Week 12 will mark Cincinnati's first game of the year without Joe Burrow under center. The first overall pick tore his ACL and MCL during last week's loss to the Washington Football Team.
Finley relieved Burrow following the injury but failed to lead a scoring drive, completing 3 of 10 passes for 30 yards and an interception. He also took four sacks against a tough Washington front.
Allen was on the practice squad and was added to the active roster on Monday. He has experience under Bengals head coach Zac Taylor as the two were on the Los Angeles Rams in 2018, when Taylor was the team's quarterback's coach.
The former sixth-round pick of the Jacksonville Jaguars made his first three career starts in 2019 for the Denver Broncos in Drew Lock's absence. He completed just 46% of his passes, tossing three touchdowns and two interceptions.
Burrow will be sidelined for the remainder of the campaign but Cincinnati expects him to be healthy for next year.