The England U21 duo were handed suspensions for incidents that happened at the end of the side's play-off game against Serbia in October.
Ince was banned for one match while Caulker was suspended for two following the altercation, which led to host country Serbia being punished for racist abuse and violent behaviour.
The FA appealed on behalf of the pair but UEFA has planned a counter-appeal requesting for punishments handed out to both England and Serbia to be increased.
Tottenham defender Caulker and Blackpool winger Ince will appear at UEFA headquarters in Nyon on Friday, accompanied by England U21 manager Stuart Pearce and two FA legal representatives.
Caulker and Ince, together with four Serbian players and two coaches, were banned after England's 1-0 win in Krusevac, a victory that ensured Pearce's men qualified for this year's finals in Israel.
Racist chants from Serbian fans towards England players followed the brawl and Serbia were ordered by UEFA's disciplinary panel to play their next competitive U21 game behind closed doors, as well as imposing a £65,000 fine.
Following the initial announcement of the bans, FA general secretary Alex Horne said: "It is the FA's vehement belief that its players and staff acted correctly in the face of provocation, including racist abuse and missiles being thrown.
"We are therefore surprised to see that two of our players have been given suspensions."