Groy, 26, is expected to sign the offer sheet Tuesday. The Bills will have five days to match the deal for Groy or allow him to join the Rams.
Buffalo gave Groy an original-round restricted free-agent tender earlier this month, worth $1.8 million. Because Groy was undrafted, the Bills will not receive any draft compensation if they decline to match the Rams' offer.
Initially a backup guard for the Bills, Groy would rejoin former Bills offensive line coach Aaron Kromer in Los Angeles and is expected to start at center for the Rams after Tim Barnes was released.