The Bills are reportedly bringing in C Dillon Day as a potential addition.
Buffalo will likely turn to Ryan Groy for the remainder of the season as their starting center.
Bodine, 26, is a former fourth-round pick of the Bengals back in 2014. He played out the final year of his four-year, $2,676,456 contract before agreeing to a two-year contract with the Bills this past March.
In 2018, Bodine appeared in 10 games for the Bills.