The proposal, however, indicated progress in talks that had appeared stalled. The person would only discuss the plan on the condition of anonymity because of the sensitivity of the negotiations.
As part of a broader budget deal, Boehner is still seeking more spending cuts than Obama has proposed, particularly in mandatory health care spending. Boehner has asked for a long-term increase in eligibility age for Medicare and for lower costs-of-living adjustments for Medicare.
Boehner's tax proposal was first reported by Politico.
A Boehner aide would not comment on the report.
At issue are expiring tax rates that would automatically increase on Jan. 1 for virtually every income tax payer if Congress and the president don't act. Steep budget cuts are also scheduled to kick in, unless Congress and Obama agree to forestall them with other deficit reduction measures.
Obama has insisted on extending current rates for the 98 percent of taxpayers in household that earn less than $250,000. He would let the top two marginal rates increase from 33 percent to 35 percent and from 36 percent to 39.6 percent for those taxpayers making over that threshold.
Until now, Boehner had maintained his opposition to raising any rates. Instead, he had proposed to raise up to $800 billion in tax revenue over 10 years by limiting tax loopholes and deductions as part of a broad tax overhaul.
But the speaker and House Republicans have come under increasing pressure form a number of Senate Republicans who say they should yield to Obama's demand on tax rates and then press him for additional cuts early next year in exchange for an increase in the nation's borrowing limit.
Obama has proposed about $600 billion in spending reductions over 10 years, including about $350 billion in Medicare and other health care savings. But he has also proposed about $200 billion in additional spending, including aid to the unemployed and to struggling homeowners and for public works projects.