McCarthy said that the president asked Congressional leaders to return on Friday after the House leadership races were complete, suggesting that Pelosi was waiting to make a deal until she became Speaker.
So far, the administration has rejected a proposal from Democrats to re-open government without money to build a wall along the U.S. -Mexico border.
Trump said he was open to working on a path to legal status for hundreds of thousands of young illegal immigrants known as Dreamers, pointing toward a potential broader deal with Democrats that could resolve the shutdown.
The partial shutdown has entered its 12th day as lawmakers remain divided on border security funding.
The two sides met Wednesday for a briefing on border security with Homeland Security Secretary Kirstjen Nielsen, the first meeting since a holiday period of inactivity during which Pelosi vacationed in Hawaii.
"Let's make a deal?" he tweeted.
In an interview with Fox News on Monday, Trump said that he was ready to end the shutdown.
Senate Republican Leader Mitch McConnell, R-Ky., and top House Republicans Kevin McCarthy, R-Calif., and Steve Scalise, R-La., attended the meeting in the high-security enclave of the White House, which typically is used to handle sensitive information.
But in the past, they supported multiple bills that proposed border barriers similar to what Trump has described as acceptable.
Pelosi said the Democrats will still vote on Thursday, as Congress starts its new session with the Democratic party in the majority in the House after victories in the midterm elections last November. He called the border a "sieve", rebutted Democratic complaints that a wall was immoral, provided an estimate of the USA illegal immigrant population far higher than the figures most experts cite and made disputed comments about progress toward building a wall. That explains Trump's sudden reversal late previous year when he refused to back a bipartisan spending package that Congress had passed with the expectation he would sign it.
The last time Schumer and Pelosi met Trump at the White House, on December 11, it turned into a freaky televised squabble during which Trump claimed he would be "proud" to shut down the government over the wall, and insisted he would take ownership of any shutdown.
Trump has been saying since at least July he'd shut down the government if Congress wouldn't deliver the wall funding.
Pelosi was nearly certain to win Thursday's House vote for speaker, a position she held for four years from 2007, when she made history as the first woman ever to rise to that post.
"I think I would have been a good general, but who knows?" he said.
Democrats said they would proceed with plans to hold votes on Thursday, when they formally take control of the House of Representatives from the President's fellow Republicans, on legislation that would end the shutdown without providing the wall money sought by Mr Trump.
Pelosi has said that Democrats will pass legislation to reopen government but not provide funding for a wall. That measure would provide money through the remainder of the fiscal year, to September 30.
The shutdown began December 22. But they have drawn the line at the use of any taxpayer money for the erection of a new wall.
It would also include another measure to fund the departments of Agriculture, Interior, Housing and Urban Development and others closed by the partial shutdown. In past shutdowns, Congress has approved retroactive pay once the impasse has been resolved.