Lee, 47, a lawyer who served as a clerk to Supreme Court Justice Samuel Alito - has said he would accept the nomination and hasn't ruled out voting for his own confirmation.
Such a judge, she said, "would not be acceptable to me because that would indicate an activist agenda".
Whoever the new justice is will pick up where Kennedy left off nearly surely will cast a more conservative vote next term. The Maine senator said she would only back a judge who would show respect for settled law such as the 45-year-old Roe decision, which has always been an anathema to conservatives. Now, it's down to six or seven being interviewed.
Hawkins noted that Kennedy has voted to uphold abortion rights in several cases, including the landmark 1992 ruling Planned Parenthood v. Casey, and more recently, in Whole Woman's Health v. Hellerstedt, which overturned a Texas law that placed additional health regulations on clinics that perform abortions.
Trump got his first Supreme Court pick after McConnell led a Republican blockade against Merrick Garland, former President Barack Obama's nominee to fill Scalia's seat.
Trump's first pick for the Supreme Court, Neil Gorsuch, is the youngest of the justices at age 50.
During his 2016 campaign and presidency, Trump embraced anti-abortion groups and vowed to appoint federal judges who will favor efforts to roll back abortion rights.
President Trump reportedly asked advisers their opinions about nominating Utah Sen.
Possible nominees being eyed include Thomas Hardiman, who serves alongside Trump's sister on the Philadelphia-based 3rd U.S. Circuit Court of Appeals, and Raymond Kethledge, a federal appeals court judge who clerked for Kennedy.
Echoing Leo's view, Sen.
"I don't even think they're going to call me", Mr. Melendez told his producer at one point, as he as he waited for the call from Mr. Trump. "And probably not. They're all saying, 'Don't do that, you don't do that, you shouldn't do that, ' but I'm putting conservative people on".
Yet Justice Kennedy's retirement, which comes as Republicans maintain a narrow majority in the Senate, may be something of a parting gift to the pro-life movement.
Krasnoff, of Planned Parenthood, said abortion-rights advocates also will be lobbying senators to vote against any nominee seen as likely to overturn Roe.
Collins appeared on ABC's "This Week" and CNN's "State of the Union", Leo spoke on "Fox News Sunday" and Graham was on NBC's "Meet the Press".
Trump's initial short list of 25 names of potential nominees was largely handpicked by The Federalist Society, an influential group of conservative lawyers.