"The President's budget that he put forward actually proposes $3 trillion worth of deficit reduction over 10 years," Yellen said at a Wall Street Journal event on Wednesday.
"In this negotiation, the President has already offered changes that would result in an additional trillion dollars of deficit reduction," she added.
The savings proposed by Biden's freeze would narrow the difference between Republican and Democratic spending plans as the two sides seek an agreement to raise U.S. borrowing limits and avert a potentially catastrophic debt default.
Yellen has repeatedly said the government could run out of money to pay for its existing obligations as early as June 1. That is now eight days away.
Yellen's comments suggest the two sides are moving closer together on the top line figure, although significant disagreements remain about how the deficit reduction would occur.
The Republicans say their spending plans would cut the deficit by $4.8 trillion over a decade, but insist there should be no cuts to the defense or border security budgets.
The White House says any cuts to the deficit should apply more broadly to reduce the burden on individual departments, and wants to raise some taxes to fund the deficit reduction - which Republicans have so far opposed.
The additional trillion dollars in savings proposed by the president would be realized over the next 10 years, according to the person familiar with the talks.
Other areas of compromise from the president include proposals to rescind unspent COVID-19 relief funds, the person said.
Negotiations continue Wednesday on the debt limit. This story will be updated as new developments take place.