In a brief statement, Premier League leaders City said the appeal would be heard before Wednesday's League Cup semi-final against Liverpool at Eastlands.
If an appeal is rejected, City will be without star defender Kompany for both legs of the semi-final and league games against Wigan and Tottenham.
Kompany was, controversially, shown a straight red card by referee Chris Foy in the 12th minute of Cup holders' City's 3-2 third round loss at home to United on Sunday for a two-footed tackle on Nani even though he won the ball cleanly.
City, already 1-0 down to an early Wayne Rooney goal, were 3-0 behind at the break after further goals from Danny Welbeck and Rooney.
However, despite being down to 10 men, they hit back in the second half through Aleksandar Kolarov and Sergio Aguero.
But it was not enough to prevent a defeat in the third round -- the stage at which top-flight clubs enter the FA Cup - and with it the defence of the trophy City won after beating Stoke in last season's final.
City lead reigning champions United by three points at the top of the Premier League table.