Monday's announcement marks the first time the agency publicly has discussed the possibility of putting surplus animals to death.
The agency is also considering whether to stop roundups of wild horses to save money, a move that would be criticized by and from sheep and cattle ranchers who see the mustangs as competition for feed on the open range.
"Our goal is supposed to be about healthy horses on healthy ranges. But we are at the point we need to have a conversation with people about pragmatically what can we do given the financial constraints of our program to meet the goals we have," Bisson said.
There are an estimated 33,000 wild horses on the range in 10 Western states, Bisson told the organization's National Wild Horse and Burro Advisory Board. About half of those are in Nevada.
The agency has set a target "appropriate management level" of horses at 27,000.
About another 30,000 horses are in holding facilities, where most are made available for adoption. But those deemed too old or otherwise unadoptable are sent to long-term holding facilities to live out their lives -- some for 15 to 20 years.
The board will consider the alternatives at its next meeting in September.
Last year about $22 million of the entire horse program's $39 million budget was spent on holding horses in agency pens. Next year the costs are projected to grow to $26 million with an overall budget that is being trimmed to $37 million, Bisson said.
"We have a responsibility to balance the budget, so we are going to have to make some tough choices," Bisson said.
Bonnie Matton, president of the Wild Horse Preservation League, said she wasn't surprised by the agency's predicament.
"They really do have a can of worms," she said.