This, after the club put on six free coaches for fans for their second round replay.
The Robins, who drew 1-1 with their rivals to set up the replay, will head to Edgar Street looking for their first win over Hereford since 1999 hoping to match the 1336 Bulls who made the journey on Monday.
"The club felt that in view of the huge importance of the game, we'd like to encourage as many fans as possible to travel to Hereford," Cheltenham chairman Paul Baker told the Gloucestershire Echo.
"We traditionally take a lot of fans to Hereford, but Christmas is approaching and people may be reluctant to spend money.
"I think it's a great gesture from the club to lay on the free coaches and I hope the fans respond in great numbers.
"Hereford's support was fantastic on Monday and we need to replicate that at their ground now."
The free seats on the coaches for the 40 mile trip to face the Blue Square Premier side are available on a first come first served basis.
Everton, sixth in the Premier League, will make the trip to the winner in the third round on Monday January 7.