With the number of migrants coming across the border continuing to surge, the Biden administration is reportedly preparing to vaccinate migrants coming into U.S. custody -- amid continued fears of a risk of COVID-19 spreading between migrants, law enforcement and the American public.

The Washington Post reported Tuesday that the Department of Homeland Security (DHS) plans to vaccinate migrants as they come into custody for processing by Customs and Border Protection (CBP). 

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Vaccines would also be offered to those facing deportation, but not to those being quickly expelled via Title 42 public health protections, the outlet reported. The vaccines used would be the single-dose Johnson & Johnson vaccine.

So far, the vaccine has been administered to migrants in Immigration and Customs Enforcement (ICE) custody, although Fox News reported last month that 30% of immigrants in ICE custody are declining the shot.

DHS, in a statement to Fox, said its protocols had not yet changed.

"The health and safety of our workforce and the migrants in our care are of paramount importance," a spokesperson said. "We continue to monitor and reassess our COVID-19 protocols.  At this time, our protocols have not changed."

The report comes as border states have expressed concern about the potential risk of COVID-19 transmission coming from migrants being kept in cramped conditions, both on their way to the border and on arrival, before often being released into the country.

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Texas Gov. Greg Abbott last week issued an executive order for law enforcement to pull over vehicles carrying migrants due to the risk of COVID-19 transmission. The Department of Justice sued and won a temporary injunction against Texas on Tuesday.

"The Biden Administration has knowingly — and willfully — released COVID-19 positive migrants into Texas communities, "risking the potential exposure and infection of Texas residents," Abbott’s office said in a statement. "The Governor’s Executive Order attempts to prevent the Biden Administration from spreading COVID-19 into Texas and protect the health and safety of Texans."

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Meanwhile, a top Border Patrol union official warned that agents are being forced to release COVID-positive migrants "day in, day out" and not all are being tested. He said it is a risk not only to the public, but also to agents.

"We have a lot of agents quarantined right now, which adds to our problem, on top of agents who are sick with COVID, so we’re concerned about catching it ourselves, we’re concerned about our families and coworkers and it just seems everyone's turning a blind eye to it when we have a real situation down here," Chris Cabrera, a vice president of the National Border Patrol Council, said Saturday on "Fox News Live." 

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More than 188,000 migrants were encountered in June, marking the latest month for numbers to rise. That number is expected to rise beyond 200,000 in July, with the Associated Press reporting that preliminary estimates put the number at 210,000.

The Biden administration had reportedly been considering ending Title 42 health protections, which allow for the rapid expulsion of migrants due to the COVID-19 threat. It has not been applying the Centers for Disease Control (CDC) order to unaccompanied children and many migrant families with children under 7.

However, this week the CDC announced the order was, in fact, being extended.

Fox News' David Aaro contributed to this report.