Under the broad outlines of the new plan, the Department of Homeland Security will vaccinate the migrants soon after they cross into the United States and await processing by US Customs and Border Protection, said the Post, which cited two unnamed DHS officials.
Until now, only a limited number of migrants have received the vaccine while held in longer-term US Immigration and Customs Enforcement detention facilities, the Post said.
The plan has not yet been finalized, the paper said.
Asked about the report, a DHS spokesperson said: "We continue to monitor and reassess our COVID-19 protocols. At this time, our protocols have not changed."
U.S. authorities have stepped up efforts to persuade more people to be vaccinated against the coronavirus as the number of COVID-19 cases rise. They also face increasing numbers of migrants crossing from Mexico.
Record numbers of unaccompanied children, more than 19,000, were likely encountered by border patrol agents in July, and overall apprehensions of migrants are on pace to be the highest ever recorded this fiscal year, a top DHS officials said in a court filing Monday.
As of Saturday there were about 72,000 new COVID-19 cases per day in the United States, a 44% increase over the previous week, according to the U.S. Centers for Disease Control and Prevention.
The Post reported one of the officials as saying the vaccines would be provided to migrants facing deportation as well as those likely to be released into the United States pending a court hearing.
Vaccines will not be offered, at least initially, to migrants sent back quickly to Mexico under the so-called Title 42 order without the chance to seek asylum or other protections in the United States, the Post said.
Health authorities in northern Mexico vaccinated hundreds of migrants living in makeshift tents close to a pedestrian crossing bridge to the United States in the border city of Tijuana on Tuesday.