The White House wants leaders from Canada and Mexico, the other two members of the trade deal, to announce the framework of an agreement at the Summit of the Americas in Peru, which starts April 13, Bloomberg reported. Negotiators would have to finish final details of the new plan later.
The Trump administration would like to see changes, particularly in the automotive industry, but two weeks "is probably too optimistic," a White House official who declined to be named told CNBC. The official called that deadline "a marker that we'd like to see something done by."
Representatives from the three countries have negotiated the workings of a revised agreement for months. Trump has repeatedly criticized the deal, arguing it hurts American workers by pushing jobs out of the country.
He has threatened to pull the U.S. from the agreement if the three nations cannot improve it.
During a string of tweets about immigration policy Monday morning, Trump took another swipe at the trade deal, saying Mexico "is making a fortune" from it.
The report comes amid a string of trade actions from the Trump administration. Last week, the White House said the U.S. reached a tentative major trade deal with South Korea, which Trump subsequently threatened to delay.
This week, he is also expected to announce a list of Chinese imports the U.S. plans to target with tariffs.
A White House spokeswoman declined to comment on the Bloomberg report.
— CNBC's Eamon Javers contributed to this report