The Centers for Disease Control and Prevention (CDC) said the revised timeline would help to “make international travel as safe as possible” amid growing concern over the spread of the new strain.
Currently, vaccinated international air travellers can present a negative antigen test result obtained within three days from their point of departure. Nearly all foreign nationals must be vaccinated to enter the country.
Unvaccinated travellers currently must get a negative Covid test within one day of arrival.
The stricter rules could be announced on Thursday, but it is unclear when they might take effect.
CDC Director Rochelle Walensky said the agency "is evaluating how to make international travel as safe as possible, including pre-departure testing closer to the time of flight and considerations around additional post-arrival testing and self-quarantines".
He stressed there was no need for lockdown restrictions “for now… if people are vaccinated and wear their masks”.
Last month, Mr Biden’s administration lifted a sweeping travel ban imposed by his predecessor Donald Trump at the beginning of the pandemic which covered swathes of Europe, including the UK.
But he vowed to cooperate with other countries on future travel restrictions. “Unlike [Donald] Trump I don’t shock our allies,” he said.
The US, along with many countries in Europe and the UK, has banned all travel from several countries in southern Africa over fears about the new strain.
On Tuesday, the CDC advised Americans against travel to Niger, Papua New Guinea, Poland, and Trinidad and Tobago, citing Covid concerns.
A White House official said the administration is evaluating Covid measures “including more stringent testing for international travel”.
A CDC spokeswoman confirmed the agency is working to modify its global testing rules for travel "as we learn more about the Omicron variant; a revised order would shorten the timeline for required testing for all international air travelers to one day before departure to the United States."
The CDC now lists about 80 foreign destinations as having “Level Four,” its highest level of Covid transmission, and discourages Americans from traveling to those destinations.