President Biden is using a Trump-era rule to curb Venezuelans from entering the US at the southern border.
Title 42 was invoked in 2020 under Trump to send migrants back to Mexico, citing the COVID-19 pandemic.
Biden's Justice Department, however, has been fighting the policy in court.
According to the AP, Mexico has said it would only take in one Venezuelan migrant for each Venezuelan allowed to enter the US on humanitarian parole.
Under the current policy, Venezuelan migrants who walk or swim across the border will be expelled and those who illegally enter Mexico or Panama won't be able to enter the US, DHS said.