It is also expected to include a weekly unemployment boost of US$300 ($396) until March, as well as billions of dollars for the distribution of COVID-19 vaccines and support for schools and small businesses.
Republican Senate leader Mitch McConnell said: “We made major headway for hammering out a targeted relief package.”
Democratic Senate leader Chuck Schumer said: “It’s not a done deal yet. But we are very close.”
President-elect Joe Biden said the prospects for a deal were “encouraging”, saying: “It looks like it’s very, very close.”
He described the potential package as a “down payment” and said he would push Congress to pass another round of stimulus after he is inaugurated on January 20.
Democratic Senator Bernie Sanders said he was still pushing for US$1200 cheques to be sent to all Americans who earn under US$75,000 a year, the same amount as earlier in the year.
In a call with Republicans, McConnell said that passing a package before Christmas could help the party win the two crucial Georgia Senate run-off contests on January 6.
He said Republicans Kelly Loeffler and David Perdue were “getting hammered” for Congress’s failure to deliver more financial aid to struggling Americans – especially the politically-popular direct payments.
The US poverty rate jumped to 11.7 percent in November, up 2.4 percentage points since June, according to new data released by researchers at the University of Chicago and the University of Notre Dame.
The federal poverty line in America is US$26,200 ($35,600) for a family of four.
The average unemployment payment was more than US$900 a week from late March through the end of July, but it fell to about US$300 a week in August when expanded benefits expired.
Food banks around the country have been struggling to cope with a surge in demand as the pandemic has continued. One in eight Americans reported they sometimes or often did not have enough food in November, according to a census survey.
Matthew Knott is North America correspondent for The Sydney Morning Herald and The Age.