The proposal would provide a steady funding source to the IRS, after years of flat or declining budgets forced steep cuts in the number of employees conducting audits and collecting money. Agency officials have said they need a multiyear commitment from Congress so they can hire and train enforcement staff and ramp up audits with less risk of lawmakers stopping such an initiative midway through. The money would let the IRS increase its enforcement staff by about 15% a year.

The Treasury Department’s career staff estimates that more than half of the $700 billion in additional revenue would come from changes to how businesses’ and individuals’ income is reported to the government, the people said. Under the plan, banks and other payment providers would be required to tell the IRS how much money came into and out of individuals’ and businesses’ accounts each year, going far beyond the existing reporting of interest income.

That change wouldn’t require individuals and business owners to file any additional forms, and it wouldn’t provide the IRS with direct information about what someone’s tax liability should be. Business owners trying to hide income could still attempt to use cash or cryptocurrency, both areas that the IRS has struggled to police.

But the change to the information-reporting rules would give the IRS much more information about business income as it decides who to audit. It would also create an enormous flow of information that the IRS would have to learn how to manage and use.

About $30 billion of the funding boost would pay for technology upgrades and other changes, some of which makes sure the IRS could obtain and analyze the bank information, the people said.

When the government has independent information about income—such as W-2 forms with wage data—compliance rates are nearly 100%. Where it doesn’t have such information—much of business income—estimated compliance rates are often about half that level.

Congress will have to weigh the potential burdens and privacy concerns against the revenue gains as it considers the plan.

The proposals are expected to be included in the roughly $1.8 trillion antipoverty plan that Mr. President Biden is set to detail Wednesday in a speech to Congress. The additional money from tax enforcement and higher tax rates on high-income households would pay for an extension of the expanded child tax credit along with programs to expand child care and funding for community college.

The antipoverty plan is likely to also include a proposal to raise capital-gains taxes and change how unrealized gains are taxed at death as income, but is unlikely to include a change to the estate tax, which applies to the total net worth of wealthy people who die.

Generally, the idea of collecting money the government is already owed is appealing to both parties because it doesn’t require tax increases that could dampen economic growth—and because it is easier to sell such policies to the public as getting money from people who should have been paying all along. But businesses and individuals who face more intense audits have a long history of complaining to their representatives when enforcement ramps up.

Democrats, who have been building political support for a significant IRS expansion, welcomed the proposal.

“For too long, working families have footed the tax bill for America’s billionaires and corporations,” Rep. Peter DeFazio (D., Ore.) said on Twitter. “I’m proud to be working [with President Biden] to ensure the IRS has the funding to ensure the wealthiest pay their fair share & to provide basic taxpayer services.”

Before Congress considers this proposal, it should make sure the IRS has appropriate oversight so there are safeguards as law enforcement expands, said Pete Sepp, president of the National Taxpayers Union, a conservative-leaning taxpayer-rights group.

“No one has properly assessed the risks of this proposal, thinking that it’s some magical pot of gold at the end of the rainbow,” he said. “They’re not ready for it. The taxpayer rights protection structure is not ready for it. They have not adequately thought through how and where this money can be best spent.”

The New York Times reported some details of the plan earlier Tuesday.

“The plan is excellent in that it’s comprehensive both on the funding side and on the information reporting side,” said Chuck Marr, senior director for federal tax policy at the Center on Budget and Policy Priorities, which advocates for spending much more money on IRS enforcement.

The IRS has been shrinking steadily for the past decade after a series of budget cuts, and Democrats have been relatively united around trying to reverse the trend. The agency’s $12 billion budget is about what it was in 2010, despite inflation, population growth and increased responsibilities. Republicans have been less interested in major expansions, but they generally aren’t backing further cuts.

Audit rates of individuals have hit 40-year lows, and the agency has 15% fewer employees than it did in 2010. The IRS says it devotes 30% less funding and staff to enforcement than it did in 2010.

The agency estimates that for tax years 2011 through 2013, about $381 billion annually in legally owed taxes went uncollected—in what is known as the tax gap. After inflation and budget cuts, that number is now likely much higher. IRS Commissioner

Charles Rettig

told Congress earlier this month that the figure could be as high as $1 trillion a year, though the administration’s estimates assume a lower amount.

Nonpartisan analysts project that additional money for IRS enforcement would more than pay for itself.

“The risks are that they screw it up in the execution. The risks are that administrations change priorities,” said former IRS commissioner Fred Goldberg, who has been advocating for more funding. “All of those things can happen, but the good things can happen too and if you don’t take a shot at it, it’s never going to happen.”

The administration’s goal is to focus enforcement on the highest-income Americans, the people familiar with it said, adding that audit rates for households with actual income under $400,000 would remain similar to what they have been in recent years. The plan doesn’t set target audit rates for higher-income households, giving the IRS flexibility to decide where to focus its attention.

The administration’s proposal for multiyear funding will be welcome at the agency, where officials emphasize that they need consistent funding. It can take years to hire and train skilled investigators and then years after that for their efforts to yield money as they battle high-income taxpayers.

The certainty of that multiyear funding can let the agency plan better and makes the plan doable, Mr. Goldberg said.

“Enforcement alone will not narrow the Tax Gap, and the efforts necessary to raise compliance levels are resource intensive for the IRS and can be intrusive to taxpayers,” Mr. Rettig wrote this month on the IRS website. “We are committed to working with our partners to carefully balance the need with the burden.”

Write to Richard Rubin at richard.rubin@wsj.com