The forward joined Watford last month with the price to be decided by a tribunal after the Cumbrians rejected an initial £25,000 offer for the former Middlesbrough man.
That tribunal has now been postponed as Watford have a pre-season friendly on the arranged date of July 27 and Carlisle owner John Nixon is keen to get the matter resolved.
"We turned bids down earlier in the season simply because we valued the player at a much higher level," he told BBC Sport.
"We have had other offers since then and they still haven't matched what we expected to get so we were keen to get the issue resolved at a tribunal later this month. Obviously it is disappointing it has now been postponed but we hope to get a new date fixed sooner rather than later."
United turned down a bid of £250,000 from Huddersfield for Graham in January and are thought to be keen to get a similar fee from the Hornets.