House Democrats and the Trump administration are near a deal on to replace the North American Free Trade Agreement after more than a year of deliberations, sources told CNBC.

If the White House sends ratifying legislation to Congress by Dec. 15 to kick off the approval process, the Democratic-held House could vote on ratifying the United States-Mexico-Canada Agreement by Dec. 18, two sources informed by the White House tell CNBC. House Speaker Nancy Pelosi will make the final scheduling determinations, and the USMCA vote could come in the immediate aftermath of a vote on articles of impeachment against President Donald Trump, these sources said.

Earlier Monday, two senior Democratic aides said the sides were close to an agreement but had nothing to announce yet. The Trump administration delivered proposed changes to House Speaker Nancy Pelosi's office on Saturday, and House leaders were still studying them.

Senate Finance Committee Chairman Chuck Grassley, R-Iowa, also spoke to U.S. Trade Representative Robert Lighthizer on Monday and is "hopeful there will be an announcement on a deal soon," the senator's spokesman Michael Zona said. Grassley expects the Finance Committee will get formally briefed on trade developments later this week, he added.

The White House has pushed for USMCA's approval in Congress before the end of the year as Trump seeks an economic and political win before the 2020 election. Democrats, who have sought tougher enforcement of labor rules to ensure U.S. companies do not move jobs to Mexico, have tried to show they can legislate even as they move forward with an impeachment inquiry against Trump.

When lawmakers receive the bill, it starts a 90-day window to pass it. Some sticking points seemed to remain over the weekend.