Now, though, it appears Graham is keen on finding a new deal that the U.S. can bring to the negotiating table.

It is unclear how far along the team is in crafting a proposal, but Graham did travel to Israel earlier this month to meet with officials about the situation with Iran.

In an interview with The Daily Beast on Wednesday, Graham said he had spoken to Trump about his ideas for a new nuclear deal several times and that the president was contemplating them. The senator said the U.S. should ask the Iranian regime to agree to a so-called 123 Agreement—a key, legally binding commitment that requires countries doing nuclear deals with the U.S. to sign on to nonproliferation standards. The U.S. has entered into those agreements with more than 40 countries.