Trengove was suspended after a tackle on Adelaide's Patrick Dangerfield left the Crow concussed and unable to play on in last Sunday's encounter.
Dangerfield was immediately substituted off.
The Demons will appeal based on their claim that the evidence presented was unreasonable, the offence classification was manifestly excessive and the sanction was manifestly excessive.
He was initially suspended for two weeks by the match review panel but the sanction was compounded when he unsuccessfully challenged it at the tribunal on Tuesday night.
The Demons had called expert witnesses Kelly O'Donnell, the club's tackling coach, and bio-mechanist Dr Kevin Ball as part of their unsuccessful defence.
Tribunal counsel Andrew Tinney SC argued that by grabbing Dangerfield's arm and keeping hold of it throughout the tackle Trengove had not exercised his duty of care to his fellow player's safety.
Tribunal members Emmett Dunne, Wayne Henwood and Wayne Schimmelbusch dismissed the Melbourne legal team's challenge leading to an outpouring of sympathy from Trengove's teammates.
A number of Melbourne players vented their frustration via Twitter.
Brad Green, James Frawley, Colin Sylvia, Luke Tapscott, Cale Morton, Nathan Jones and Jack Watts all voiced their disapproval of the decision.
The appeal will be heard at 5.30pm on Thursday.
