National Game have rejected Arsenal's proposal that teams who qualify for the FA Cup Final should be allocated more tickets than their usual quota of 25,000.
The Gunners have been running a campaign to enable more fans to attend the annual Cup final at Wembley Stadium.
An Arsenal spokesman said: "Whether or not we reach the FA Cup final, we feel strongly that as many supporters as possible of the two teams should enjoy the big day."
But National Game directors on the Football Association board have opposed the idea that would see county Football Associations give up their share of 23,000 tickets.