Hull FC admit fixture congestion means that they face problems rearranging the postponed fixture at Catalan Dragons.
The original fixture was postponed four hours before kick-off due to a frozen pitch in Perpignan last Saturday.
Hull's Communications Manager James Clark told BBC Look North: "Both clubs are hoping for a significant cup run, we certainly are.
"But, if that isn't the case and both clubs are knocked out, a Challenge Cup weekend is an option."
Around 300 Hull fans made the trip to France, many paying in excess of £300 for their travel arrangements.
The club promised that they would work with the Catalans when the game is rearranged to try and find a range of options that would offer supporters the best travel deals.