McClain, who stands at 6-foot-5, 336 pounds, has not appeared in a game this season. He spent all of last season on the Baltimore Ravens' practice squad after being signed as an undrafted free agent from Clemson.
The Bills were using Young, who can play both tackle and guard, as their top backup guard until offensive lineman Doug Legursky returned last week from a knee injury.
Legursky was active for the first time this season but did not play in Thursday night's loss to the Cleveland Browns.
Head coach Doug Marrone said Monday that Legursky will now compete with Colin Brown for the starting job at left guard, continuing a battle that began in training camp.
"We do need to improve our play there. That's going to be an open competition," Marrone said. "Both of those players will play at left guard this week against Cincinnati. How we're going to do it, we still haven't finalized that plan. By quarters, by series, whatever it may be, that we're going to work out during the week with the players and what the best situation for all of us to get the stuff out there."
Marrone did not rule out continuing the left guard-by-committee approach, as long as it produces the right results.
"I want that position to play better now. And if two guys playing that position gives us better production, then that might be the way we go. I don't have a problem with that," he said. "If one guy clearly separates himself while they're playing, we'll be able to watch that and see that. I don't have a problem playing one. But that's a position that obviously we need to get more production from."
It's unclear if McClain will factor into the competition at all. With eight offensive linemen on their active roster, McClain may be inactive on game days.