Delap was shown a straight red card in the game against Crawley after he put in what looked to be a fair challenge on David Hunt.
The referee was signalling for a throw in before the fourth official and Crawley manager Steve Evans kicked off.
Stoke have now had time to study the evidence and after doing so they have decided that an appeal will be well worth taking and the Football Association have been notified of their intentions.
The Club now have 24 hours to present their evidence to the FA.