PROVIDENCE, R.I. >> The U.S. military is looking into allowing all of the nation’s veterans who served honorably to shop online at exchanges that sell discounted, name-brand goods — a perk that is currently available only to a small minority.

The change is proposed by the Army & Air Force Exchange Service director as a way to show appreciation for veterans and to offset a loss of revenue as troops return from overseas, where they had few alternatives but to shop at the military retail stores.

For now, the online shopping is generally limited to current service members, veterans who served for 20 years or longer and their family members. Tom Shull, the director of the exchange service, said 20 million veterans would be affected if the Defense Department allows all veterans who served honorably to use the shopping website.

Veterans who use the site typically save 25 percent or more and do not pay a state sales tax. Top-selling brands include Michael Kors, Under Armour and Levi’s. Levi’s jeans for children are $15 to $20 a pair versus $28 or more in department stores.

In his seven years in the Army, Aleksandr Morosky deployed once to Kosovo and twice to Iraq. He said former service members have not asked for shopping privileges because they accepted that they are not entitled to the benefit. But if the policy changed, Morosky, 34, said he would use the site, and he thinks many other people would, too.

“I think that this makes a lot of sense,” Morosky said. “I think it would be good for everybody involved.”

Shull is adding more name-brand products and revamping the website, which last year broke even. He said he hopes to invite all veterans who served honorably to begin shopping online on Veterans Day in 2015.

Shull said it is coincidental that he proposed his idea during the Department of Veterans Affairs scandal over long waits for patient care and falsified records covering up the delays at hospitals and clinics nationwide. He said he thought of it a year ago. And while it would benefit those who have been affected by the current challenges within the VA, Shull said, he did not suggest it for that reason.

U.S. Sen. Richard Blumenthal, a member of the Senate Veterans’ Affairs Committee, said, “It’s a good idea. We should do it, but not view it as a way to make up for the VA’s failings.”

“Many, many veterans have not served a full 20 years but have nonetheless contributed immensely to the defense of our nation,” said Blumenthal, D-Connecticut. “That service ought to be recognized more fully.”

Former Army Sgt. Maj. Kenneth Preston, who retired in 2011, said he too supports Shull’s proposal because “we have asked a lot from these young men and women.” Both the Navy and the Marine Corps said it would be premature to comment.

The Defense Department says it must weigh whether the policy change would diminish the benefit for current patrons, cost the department more, or harm other local businesses and tax collection. It historically has not supported expanding the benefits that are designed to recruit and retain service members, and has scrutinized how any changes would affect the entire benefits package.

There are about 2 million people nationwide who served at least 20 years in the military, according to the Defense Department.

Shull, who is the first civilian director of the exchange, suggested letting veterans from all of the branches who served honorably use the exchange website but not the brick-and-mortar stores. He expects less revenue from the physical stores as troops return from overseas, and he worries people won’t shop on U.S. bases as much in the coming years if commissaries, or grocery stores, raise prices because of budget cuts.

Shull said he needs to boost profits so the exchange service can continue to pay for programs for service members and their families on Army and Air Force bases.

Headquartered in Dallas, the exchange did $8.3 billion in sales in 2013 and netted $332 million in earnings, its data shows. It gave $208 million of its earnings as a dividend to the Army and the Air Force for Morale, Welfare and Recreation programs, including family counseling and youth services. Online sales could grow from about $200 million annually to $1 billion by 2019, Shull said.