A source told ESPN's Field Yates that the pick is a conditional seventh-round selection.
McCray was one of only two free agents to sign with the Packers this offseason who had played for another organization the season before.
McCray appeared in 11 games for the Denver Broncos last season, finishing with seven tackles and a 1/2 sack.
The Bills have a need at linebacker after injuries to their first two selections in the 2016 draft.
Bills rookie linebacker Reggie Ragland, picked in the second round to start at weakside linebacker, is expected to miss the entire season after tearing the ACL in his left knee.
Shaq Lawson, the team's first-round pick who was slated to start at outside linebacker, underwent shoulder surgery in May, and was expected to return between Week 6 to Week 8, a source has told ESPN NFL Insider Adam Schefter.
The Bills placed Lawson on the physically unable to return list on Tuesday, meaning the earliest he now could return is Week 7.
NFL teams have until 4 p.m. on Tuesday to trim their rosters to 75 players.