Any such crackdown would be hugely controversial, with immigration one of the hottest topics in the 2016 presidential campaign, and rights groups expressed grave concern at the deportations.
The flow of families and unaccompanied children crossing into the United States from Mexico slowed this year, but the numbers surged upwards again in October and November.
Several Latin American countries are in the grip of violent lawlessness and the El Nino weather pattern has plunged a number of countries in the region into drought.
According to the reports, hundreds of families living in the United States whose asylum requests have been denied will be rounded up and sent home.
DHS Immigration and Customs Enforcement spokeswoman Gillian Christensen told AFP that Homeland Security Secretary Jeh Johnson "has consistently said our border is not open to illegal immigration.
"If individuals come here illegally, do not qualify for asylum or other relief, and have final orders of removal, they will be sent back consistent with our laws and our values."
Republican presidential hopefuls including frontrunner Donald Trump - who took to Twitter to claim credit for the deportations - are vying for who can promise the toughest stance on immigration.
Trump tweeted: "Wow, because of the pressure put on by me, ICE TO LAUNCH LARGE SCALE DEPORTATION RAIDS. It's about time!"
In contrast, Hillary Clinton's campaign said the Democratic frontrunner has "real concerns."
Clinton "believes it is critical that everyone has a full and fair hearing, and that our country provides refuge to those that need it," read a statement reported in US media.
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