The congressional leaders spoke on the phone “about their shared commitment to completing an omnibus [spending bill] and Covid relief as soon as possible,” said Ms Pelosi’s spokesman Drew Hammill on Twitter.
Politicians are set to leave Washington DC for the festive recess on 11 December.
Ms Pelosi had talks with treasury secretary Steve Mnuchin before the 3 November election but no deal was achieved.
She and Senate minority leader Chuck Schumer have lined up behind a $908bn bipartisan spending package as the starting point for talks.
GOP leader Mr McConnell, who says he is “hopeful” of a deal has backed a more slimline $500bn package.
An estimated 12 million Americans will lose unemployment benefits after Christmas if a new deal is not agreed.
A surge in virus cases across the US have resulted in a spike in hospitalisations and new economic restrictions on businesses.
On Wednesday the number of hospitalisations passed 100,000 for the first time in the pandemic and more than 270,000 people have been killed.
In response state’s such as Ms Pelosi’s California have tightened up virus restrictions and implemented nighttime curfews for non-essential workers.