Locals have been trying to save the stencilled work after it was claimed it had been sold and would be removed.
Robin Barton, from the Bankrobber gallery in London, said "pressure is growing on the owners" to accept a seven-figure deal from an American.
The artwork, depicting men "snooping" on a telephone box, appeared in April.
Banksy later admitted painting the work on a house three miles from the government communications headquarters, GCHQ.
Last week, businesswoman Angela DeSouza failed in an attempt to raise Â£1m within a self-imposed six-hour deadline to make an offer.
But she refused to give up and has continued to gather financial pledges and negotiate a "much more reasonable" deal.
Mr Barton, who said he been asked by the owner of the house to oversee negotiations, added: "Whilst the owners are sympathetic to the community's wishes they cannot see a clear compromise that would leave them unimpeded by the presence and responsibility of owning the building and its associated mural.
"The mural has become something of a poisoned chalice and, as such, whilst they would rather it remained in situ, the temptation to pass the problem on is tempting."
Cheltenham's "Spy Booth" Banksy mural is "increasingly likely" to be removed after efforts by local businesses to save it stalled.