The plan is under consideration and no final decisions have been made, according to the officials, who spoke to The Associated Press on the condition of anonymity because the plan hasn't been announced.
The officials said the president has authority to take such action in a pandemic and that Mexico's efforts to stop the spread of the coronavirus, along with Venezuela's, have been the weakest in North and South America.
Mexico, which had no immediate comment on the U.S. proposal, has been slow to adopt public-distancing policies and cancel events, though that is starting to change.
President Andrés Manuel López Obrador finally asked people Tuesday to limit their attendance at an upcoming appearance following criticism that his crowded, touchy-feely public events contradict officials' admonishments that Mexicans begin social distancing to contain the spread of coronavirus.
Last weekend, López Obrador was seen hugging, kissing, shaking hands and posing for selfies amid large and packed crowds while touring towns in the southern state of Guerrero. And the same weekend, authorities allowed a large-scale pop concert to go ahead in Mexico City. But Mexican authorities have now announced school closures starting March 20.
The Trump administration's new proposal has echoes of its declarations in November 2018 that anyone who crossed the border illegally from Mexico would be denied asylum, a measure that has been blocked in court. Last month, an appeals court upheld that decision while a lawsuit moves forward.
The ban now being considered, which was first reported by The New York Times, would turn back to Mexico all people who cross the border illegally, not just those seeking asylum.
Homeland Security Department spokeswoman Heather Swift said the president was focused on protecting Americans from the coronavirus and that "all options are on the table."
Immigrant advocacy groups condemned the possible move.
"Decisions relating to the pandemic should be guided by public health officials, not by the Trump administration's long-standing agenda to close the border to refugees seeking asylum," said Eleanor Acer, Human Rights First's director of refugee protection. "The administration is using the pandemic as a pretext to advance its long-term goal of curtailing asylum rights for people fleeing persecution."
The proposal would be the administration's latest major policy shift to deter asylum and illegal immigration on the Mexican border. About 60,000 asylum-seekers have been returned to Mexico to wait for hearings in U.S. immigration court since January 2019 under its "Remain in Mexico" policy, which the Supreme Court ruled last week could stay in effect during a legal challenge.
Since November, the administration has denied asylum to hundreds of people from El Salvador and Honduras and flown them to Guatemala with a chance to seek protection there.
There were more than 851,000 arrests for crossing the border during the 2019 fiscal year, which ended Sept. 30. The proposed rule would apparently not apply to much smaller numbers who present themselves at ports of entry to seek asylum.