Reuters was not immediately able to confirm the draft independently. If correct it would an unprecedented disclosure of a draft Supreme Court opinion.
The Supreme Court and the White House declined to comment.
"Roe was egregiously wrong from the start," Justice Samuel Alito wrote in the draft opinion which is dated 10 February, according to Politico.
Four of the other Republican-appointed justices - Clarence Thomas, Neil Gorsuch, Brett Kavanaugh and Amy Coney Barrett - voted with Alito in the conference held among the justices, the report added.
"It is possible there have been some changes since then (Feb 10)," Politico reporter Josh Gerstein, who broke the story, said on MSNBC late on Monday.
After an initial vote among the justices following the oral argument, one is assigned the majority opinion and writes a draft. It is then circulated among the justices.
At times, in between the initial vote and the ruling being released, the vote alignment can change. A ruling is only final when it is published by the court.
In a post on Twitter, Neal Katyal, a lawyer who regularly argues before the court, said if the report was accurate it would be "the first major leak from the Supreme Court ever."
The court, which has a 6-3 conservative majority, heard oral arguments in December on Mississippi's bid to revive its ban on abortion starting at 15 weeks of pregnancy, a law blocked by lower courts.
According to the Politico reported it appeared based on December's oral argument that a majority was inclined to uphold Mississippi's abortion ban and that there could be five votes to overturn Roe.
The 1973 Roe v. Wade decision recognised that the right to personal privacy under the US Constitution protects a woman's ability to terminate her pregnancy.
The Supreme Court in a 1992 ruling called Planned Parenthood of Southeastern Pennsylvania v. Casey reaffirmed abortion rights and prohibited laws imposing an "undue burden" on abortion access.
Mississippi asked the justices to overturn the Roe and Casey rulings.
If Roe is overturned, abortion is likely to remain legal in liberal states. More than a dozen states currently have laws protecting abortion rights. Numerous Republican-led states have passed various abortion restrictions in defiance of the Roe precedent in recent years.
Republicans could try to enact a nationwide abortion ban, while Democrats could also seek to protect abortion rights at the national level.
Democrats said the draft opinion undermines the importance of this year's elections, in which they are seeking to maintain control of the House and Senate.
"We need to turn out the vote like we've never turned out the vote before," Democratic Representative Jamie Raskin told MSNBC. "The people need to stand up and defend democratic institutions and the rights of the people because the Supreme Court is certainly not doing anything for us."
Republican Senator Josh Hawley said, without evidence, that the leak was likely from a liberal inside the court.
"The justices mustn't give in to this attempt to corrupt the process. Stay strong," he said in a Twitter post.
New York Governor Kathy Hochul, a Democrat, said on Twitter that New York would "always guarantee" the right to abortion.
"This is an absolutely disgraceful attack on our fundamental right to choose, and we will fight it with everything we've got," Hochul said on Twitter in a reaction to Politico's report.
Justice Samuel Alito is quoted as saying Roe was wrong from the start. Photo: AFP