The defensive midfielder was shown a straight red by referee Peter Wright for a foul on visiting striker Nathan Broadhead.
The dismissal would leave the experienced Davis, 30, banned for Saturday's visit of in-form Charlton, the FA Cup trip to Carlisle the following weekend and the midweek League One game at Wigan after that.
But boss Steve Cotterill revealed that, after closely inspecting footage of the incident near the halfway line and receiving opinion from contacts in the game, he is confident in the appeal the club have submitted to the FA.
A decision is likely to be returned to Town later today (Thursday) or tomorrow.
Cotterill said: "For me it's not a red card, it's a yellow card at most.
"It's a robust challenge, definitely not serious foul play, you might turn it into a reckless challenge, but even that's a yellow card. He clearly gets the ball.
"He kicks the ball low, so his feet are not off the ground, so we have appealed. We'll know a little bit later on the answer.
"I definitely don't see that as a red card. We spent a long time yesterday putting the appeal together, sometimes it goes for you and sometimes it doesn't, we definitely feel we have a good case.
"Irrespective of whatever decision the panel make, that is worth an appeal. We definitely don't think it's a red card, I've spoken to a few people high up that would give me an honest opinion and they don't feel it's a red card."
It was Davis' second dismissal of the season, after the former Birmingham man was sent off against Gillingham in late August for a foul that led to a dugout altercation between management staff.
The Town boss has been stretched for personnel this week. He missed Elliott Bennett for Tuesday night's 1-1 draw through a one-game ban for handball, while regulars Ethan Ebanks-Landell, Aaron Pierre and Shaun Whalley were all absent through injury, as well as Josh Daniels.
Cotterill gave no further update on the fitness of captain Ebanks-Landell (hamstring) or fellow central defensive colleague Aaron Pierre (knee), though he did say a scan of Pierre's problem showed no issues. The stopper, however, is still complaining of discomfort.