According to Clarence E. Hill Jr. of the Fort-Worth Star-Telegram, "he will be the subject of conversation at personnel meetings this week."
Moore finished just 10-of-21 for 131 yards and no touchdowns against the Indianapolis Colts Saturday. He also lost a fumble in the 24-19 win.
In three preseason games, Moore is 30-of-55 (54.5 percent) with one touchdown and one interception.
What hurts him even more is the play of undrafted rookie free agent Cooper Rush. The Central Michigan product has four touchdowns and zero interceptions so far this preseason, completing 17 of his 20 pass attempts over the last two games.
Cowboys owner Jerry Jones complimented the rookie's play but wouldn't give up on Moore just yet:
"I'm just glad to see Rush taking advantage of his opportunities out there. Wouldn't want to get ahead of ourselves in any way here. And the other thing is that we still have a lot of confidence in 17 [Moore], his ability to be able to get in there when we would call on him with the personnel around him and get the ball in the right places."
Moore has been in the league since 2012 but has only appeared in three games, making two starts for the Cowboys in 2015. He threw six interceptions in that brief stretch, leading the team to an 0-2 record as a starter.
NFL journeyman Luke McCown is also on the roster but did not throw a pass last game.