They could be authorized before Wednesday, meaning the approval will likely come with days to spare before the Christmas holiday.
Three senior administration officials leaked the news to Bloomberg, which called it a "milestone" in the fight against the pandemic.
It comes in combination with the rollout of the president's new COVID-fighting agenda, which is centered on distributing 500M rapid COVID tests.
Shares in Pfizer and Merck traded lower on the day despite the news, though they have bounced off their lows for the trading day.
Pfizer's pill, Paxlovid, and Merck's molnupiravir are intended for higher-risk people who test positive for COVID. The course of treatment involves a series of pills at home over several days. The Administration is pinning its hopes on the likelihood that the drugs will help further reduce the hospitalization and death rates compared with last year.
"It's the biggest thing to happen in the pandemic after vaccines," said Eric Topol, director of the Scripps Research Translational Institute.