"I think under the surface in the Republican Party there's a great desire to get beyond the Trump era," Bolton told the Washington Post. "I think we'll see that particularly if he's defeated in November."
Bolton said he fears that the ramifications of Trump's first term in office will be damaging to the United States.
The former National Security Adviser added that it is critical to have a strong Republican Party to make the case for a strong US foreign policy.
Bolton’s book "The Room Where It Happened: A White House Memoir" was released on Tuesday and contains Bolton's descriptions of his work in the White House from 2018 to 2019.
The Trump administration sued Bolton to prevent him from publishing the book for containing classified information, but a US court allowed the publication of the book.
Trump said Bolton was attempting to retaliate because he was "disgruntled" for being fired.
Bolton has been characterized as one of the most aggressive neoconservative hawks in Washington who has consistently advocated that the United States engage in wars.