The building, which is located just off Hampton Road, faces Interstate 30, where 160,000 cars pass by every day.
He helped come up with the idea to sell the naming rights.
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"With the slumping economy, some of our donors have been paralyzed and (are) waiting to see where the market goes," Bias said.
The current facility is located on Industrial Boulevard in Dallas. The SPCA outgrown the building, and the Texas Department of Transportation has notified the group that the building stands in the way of the proposed widening of Interstate 35.
"We haven't received eviction papers, but at some point TxDOT will say it's time to go," Bias said.
The SPCA has raised nearly half of the $15 million needed to refurbish the new building into a state-of-the-art animal adoption center that will be twice the size of the Industrial Boulevard facility.
Bias said he hopes selling the naming rights will spark other high-dollar donors to get involved.