But officials estimate the cost to relocate the artwork from the M.D. Anderson Cancer Center's administration tower could reach $500,000.
The 18-story structure is scheduled to be torn down next year to make way for new facilities.
"We are working with several universities and private individuals," said Ann Hale with the Hurd La Rinconada Gallery in San Patricio, N.M., "but so far there are no real solid prospects."
She estimates the mural is worth more than $3 million.
The artwork was done in the early 1950s in the lobby of what then was the Prudential Life Insurance building.
Hurd died in 1984.