Sources say Collins specifically opposes federal Appeals Court Judge William Pryor, who once called Roe "an abomination".
Trump said he was working from a list of 25 conservative nominees the White House released last November, and the Center has requested disclosures for all of them.
"I would not support a nominee who demonstrated hostility to Roe v. Wade because that would mean to me that their judicial philosophy did not include a respect for established decisions, established law", Collins told CNN, also adding that the president had said he would not be asking nominees their opinion on the landmark case.
Justin Clark, in his position as director of the Office of Public Liaison, will oversee outreach with key constituencies, coalitions, grass-roots organizations and allies, the White House said.
It now appears that the Democrats may have Sen.
Trump said he expects to meet with two or three additional candidates, and that an announcement is planned for next Monday.
Similarly, Justice Neil Gorsuch, who Trump nominated to the Court a year ago, is widely seen as a pro-life conservative.
Trump has said he is focusing on up to seven potential candidates, including two women, to fill the vacancy being left by Kennedy, a swing vote on the nine-member court.
"During the morning, I interviewed and met with four potential justices of our great Supreme Court", he said.
Since each Supreme Court justice needs 51 votes to be confirmed, Democrats would only need one Republican to side against the nominee, assuming no Democrats break rank.
A controversial issue overwhelming the debate on the appointment of Kennedy's successor is abortion, which was legalised by a Supreme Court decision in 1973 and may come up again before the court.
Both Chief Justice John Roberts and Gorsuch have indicated broadly that they respect legal precedent.
So whether or not Trump appoints another pro-life justice to the Court, Roe v. Wade might remain in place. So far, Murkowski has stayed relatively mum on the topic, saying only that she would "carefully scrutinize the qualifications of judicial nominees" and would cast an "independent vote".
Anna Chu, vice president for strategy and policy at the National Women's Law Center, said she was concerned that a female pick could be a kind of "Trojan horse". "There are real stakes here".