IRS CEO Frank Bisignano, who has been tapped to lead the expansion of Trump Accounts, told CNBC's "Squawk Box" on Thursday that he expects every family could someday have one of the new tax-deferred investment accounts for children.

"We have the ability to enroll people very simply, and I think the objective is to have 70 million children under 18 to have a Trump Account," Bigisnano said.

So far, families have signed up 6.5 million children, according to a July 10 tally from the U.S. Treasury Department.

"We should have every family enrolled in a Trump Account," Bisignano said.

Bisignano, who also serves as commissioner of the Social Security Administration, said he has met with CEOs of tax-preparation companies to discuss their capability to distribute Trump Accounts. He also mentioned the potential for distribution through banks.

"It's a technology business, really, and I think we're going to make it simple for people to enroll," Bisignano said.

He also pointed to financial incentives — including the $1,000 federal seed money for babies born between 2025 and 2028, matching funds from employers and grants from philanthropists like Michael and Susan Dell — as a way to spur enrollment. "This is why I'm so confident about the 70 million ultimately," Bisignano said.

Earlier this month, Altimeter Capital CEO Brad Gerstner, who helped spearhead Trump Accounts, suggested during a CNBC appearance that the government could automatically enroll eligible children. "I hope that over the course over the next few months we are going to be auto-creating, with the Social Security Administration, 70 million accounts for every kid under the age of 18," he said.