A United States Customs agent waits for a northbound truck crossing the border to enter the United States from Nogales, Sonora, Mexico.

The United States Trade Representative Robert Lighthizer plans to issue the text of a trade deal with just the U.S. and Mexico on Friday, two sources told CNBC, though the sources added that the release of the text could slip into the weekend. One source said that the text will allow Canada to join onto the agreement at a later date.

The Trump administration has been hurrying to meet a self-imposed Oct. 1 deadline to strike a new North American trade deal. Mexican President Enrique Pena Nieto will leave office at the end of November.

House Ways and Means Committee Chairman Rep. Kevin Brady, R-Texas, said Tuesday that he expects that to see the full text that will be sent to Congress, as opposed to an outline.

Lighthizer, in New York Tuesday, said that that the U.S. would "go ahead" with a deal with Mexico, but left open the possibility of including Canada. He noted that the administration was "sort of running out of time."

"If Canada comes along now, that would be the best," Lighthizer said. "If Canada comes along later, that's what will happen."

Lawmakers have raised concerns about a two-way trade deal, and some have said that only a three-way pact could be approved by the Senate with a simple majority.

Sen. Pat Toomey, R-Pa., said that a bilateral agreement would require 60 votes, Reuters reported in August. In order to get the trade deal fast-tracked, "the administration must also reach an agreement with Canada," Toomey said.

Minority Leader Chuck Schumer, D-N.Y., has said that a bilateral agreement would raise "serious" legal concerns.

Business groups have also argued against moving forward with a deal that excludes Canada.

"It would be unacceptable to sideline Canada, our largest export market in the world," the heads of the U.S. Chamber of Commerce, the Business Roundtable and the National Association of Manufacturers wrote in a letter sent to Lighthizer last week, according to The Wall Street Journal.

The biggest sticking points to reaching a deal with Canada continue to be over dairy trade rules and dispute settlement.

Canadian Prime Minister Justin Trudeau told the Council on Foreign Relations on Tuesday that his focus has been "simply not escalating. Not opining. Not weighing in."

"My job is very simple. It's to defend Canada's interests, stand up for Canadians," Trudeau said.

Correction: This article has been updated to clarify that the text of the trade deal is expected to be released as early as Friday.