"Maybe there will be a breakthrough before May 12," said Corker, chairman of the Senate Committee on Foreign Relations. May 12 is the deadline for the U.S. to recertify the deal. "If there's not, I absolutely believe that he'll leave the agreement."
The United States is hoping to reach an agreement with Britain, France and Germany to address Trump's concerns about the 2015 Iran nuclear deal. Trump has been critical of the deal negotiated under former President Barack Obama, demanding it be fixed or the U.S. will withdraw the pact and sanctions will be reinstated.
Trump has opposed terms that would allow Iran to gradually reinstate its nuclear activities and accused Iran of violating the agreement. Iran has said its nuclear program is only for peaceful purposes and its ballistic missiles solely for defense.
Corker, a two-term senator from Tennessee who won't be seeking re-election, has played a key role in talks aimed at the preventing the deal from crumbling. He said a deal still could be reached if "there's a framework agreement."
But, "we've had some resistance from the EU three that we've been dealing with," he said.
Iran's nuclear deal was struck in 2015 with China, the United States, U.K., Russia, France and Germany.
Corker was an early supporter of Trump during the election and was floated as a potential running mate during the campaign. However, Corker later became critical of Trump's behavior and at one point called Trump an "utterly untruthful president."
Corker's relationship with Trump has ebbed and flowed ever since.
—Reuters contributed to this report.