Biden promised during his 2020 presidential campaign that he would cancel $10,000 debt for each borrower.

An analysis by the Federal Reserve Bank of New York says that doing so would translate to canceling $321 billion in federal student loans, or the entire balance for 11.8 million borrowers.

Last week, the president floated that idea again, which would possibly be through executive action, although it is unclear if he has the legal authority to do so.

During a White House press briefing on Monday, press secretary Jen Psaki was asked whether an income cap for any potential student relief program was being considered.

"There is," Psaki said.

"And he has talked about that back to when he ran for president," she noted.

Psaki stressed that income caps would ensure that the relief is "targeted to those graduates who have the greatest need" but noted that the White House is not yet "at the point where we have a final proposal or a final executive action or anything along those lines."

Biden said on Thursday that he was considering canceling "some" outstanding federal student loan debt, but ruled out a proposal by some Democratic lawmakers, including Senate Majority Leader Chuck Schumer (D-N.Y.) to erase $50,000 in debt for each borrower.

"I am not considering $50,000 in debt reduction, but I'm in the process of taking a hard look at whether there will be debt forgiveness, and I'll have an answer in the next couple of weeks," Biden said at a White House press conference.