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Allen, 28, started five games for the Bengals last year after Burrow suffered a torn ACL and MCL and other damage in his left knee during a game against the Washington Football Team in November.
Allen completed 63.4 percent of his passes for five touchdowns and 925 passing yards. He also threw four interceptions.
The former Arkansas signal-caller shined in a 37-31 win over the Houston Texans in Week 16, going 29-of-37 for 371 passing yards and two touchdowns.
Allen has taken the NFL field in two separate seasons. He started three games for the Denver Broncos in 2019, completing 46.4 percent of his passes for 515 yards and three scores.