Image copyright Getty Images Image caption Donald Trump has spoken to EU leaders
Former Vice President Joe Biden is working on a plan to provide a so-called “white cards” for some illegal migrants, who are willing to work.
He wants to “release money” to fund the humanitarian and legal status of people in the country.
But US officials have played down the idea, saying it would be “counterproductive” and weaken the border.
Mr Biden was part of President Barack Obama’s administration and is deeply unpopular with Mr Trump.
The Wall Street Journal reported on Friday that Mr Biden was quietly working with senior Democrats and Republicans on the plan.
The newspaper said a White House official had described the deal as a “power transfer” from Mr Obama to Mr Biden.
The US Congress has so far refused to approve additional funding for Mr Trump’s border wall – a proposal he made when he launched his election campaign last year.
According to the Wall Street Journal report, the Biden plan calls for 600,000 to 1.8 million people to be released from the country’s prisons and jails, or to receive temporary protection from deportation.
The others who want to stay in the US could receive “relief programmes” which would last for up to four years.
The paper quoted Democratic senator Richard Blumenthal saying: “If you threaten these human beings with a six-year prison sentence, you threaten human life.”
US interior secretary Kirstjen Nielsen described the idea as “deeply misleading”, saying it was similar to people who came to the US illegally to get a driver’s licence.
A US official said other countries, including Mexico, had agreed to “release people, pay for their transportation and help them fix their lives and work in America legally”.
“But we’re not going to let Washington DC force people on other countries to deal with their needs,” he added.
BBC politics correspondent Gordon Corera said the Biden plan was unlikely to be taken seriously in Washington.
He added that the US government could not afford such a move – even if money for it was earmarked.
Mr Biden, 72, was a veteran senator who also served as Delaware’s attorney general before joining Mr Obama’s team as his vice president in 2009.
During his term he gained notoriety for saying that men who call women “ho’s” on the street are “asking for it”.
Later in his term, Mr Biden accused “Republican fever swamps” of “laying the groundwork for atrocities”.