The Maine senator told ABC News Chief Global Affairs Correspondent Martha Raddatz on "This Week" Sunday that the most important trait for a potential justice is to "respect precedent."
Collins said that when she met with the president to discuss the need to fill the seat of Kennedy, who announced his retirement last week, she told him that several qualities are important, including judicial temperament, intellect, fidelity to the rule of law and "most important of all, respect for precedent."
The Republican senator, a supporter of abortion rights, said Roe v. Wade is settled law that has been established as a constitutional right.
"A candidate who would overturn Roe would not be acceptable," she said.
Collins added that she urged the president to expand the number of people he is considering for the high court beyond his initial list.
She said there are people on Trump's list she could not support "because I believe that they have demonstrated a disrespect for the vital principle of stare decisis," which is Latin for judicial precedent.
The Maine Republican added that "it would be inappropriate" to ask a judicial nominee how they are going to vote on a future case.
"A discussion of precedent, however, is very important," Collins said. "What I want to see is a nominee who, regardless of his or her personal views on the very difficult and contentious life issue, is going to respect precedent, regardless."
Collins said, "A number of judges [have told her] that good judges are always unhappy with some of their decisions but they make the right call regardless of their personal views. And that’s what I want to see in this nominee."