The midfielder was dismissed after 23 minutes against Liverpool, in a match the Toffees went on to lose 2-0.
Referee Martin Atkinson showed the 20-year-old a straight red after a challenge on Luis Suarez, but television replays appeared to show Rodwell won the ball and made minimal contact with the Uruguayan.
Suarez went down heavily following contact with Rodwell, but the striker's reaction was criticised for being excessive in some quarters.
Everton, having reviewed the incident, now feel they have a chance of getting the decision reversed and will submit written documentation to the FA.
Chief executive Robert Elstone told the club's official website: "Following a review of the video evidence we believe the decision to be wrong and we will be contacting the FA requesting that the red card is rescinded."
If the disciplinary panel uphold the decision, Rodwell will serve a three-match ban, missing matches in the Premier League and Carling Cup against Chelsea as well as the trip to Fulham.
Everton boss David Moyes had originally questioned Atkinson's decision in his post-match comments, suggesting that far from being a red card offence, it was not even a foul.
"There are a lot of questions that people ask about derbies, tackles and sendings-off but that wasn't down to a bad tackle," Moyes said.
"I would have been disappointed if it had been a free-kick and if he had given a yellow card you would have said 'what is that for?'."