Middlesbrough have offered to buy fans who travelled to the abandoned fixture at Ipswich Town tickets for the rearranged game.
Ipswich have offered a 50% discount to supporters who attended the initial match, with Boro making up the additional cost for their 730 fans.
Supporters saw 37 minutes of football at Portman Road before referee Dean Whitestone called the game off.
The club are also considering running a free coach for those who travelled.
Boro chief operating officer Neil Bausor said: "This is a way of thanking the fans for their continued loyalty. Our travelling support this season has been absolutely magnificent.
"The manager and the players all very much appreciate the fantastic backing they give us and the considerable sacrifices they make in terms of their time and their hard-earned money in order to do so."
Despite the disappointment, manager Tony Mowbray backed Whitestone's decision to abandon the game.
"The referee's a young guy who had to make a tough call today," Mowbray told BBC Tees.
"We were here at 11 o'clock and the pitch was under the dome and seemed playable, but coming back at quarter to two we were able to walk along the touchline and I felt it was going to be difficult to play the game.
"We were here to play; I was conscious of trying not to emphasise that we wanted the game off.
"It would have been easy for me to stamp my feet and say we want it off because Ipswich people were aware we played extra-time on Wednesday night, and we had some pretty serious quality footballers unavailable.
"He's got the right decision in the end."
No date has been set for the match to be replayed.