However, the most serious consideration was given to a handful of women candidates, and it was an Arizona judge and former state legislator, Sandra Day O'Connor, who was eventually chosen by the president.
Oaks, a former Brigham Young University president, left the Utah court in 1984 to become a member of the Quorum of the Twelve Apostles for The Church of Jesus Christ of Latter-day Saints - a lifetime appointment.
Bruce Fein, then an associate deputy attorney general, said people like Oaks and future nominee Robert Bork were researched, but they were second-tier prospects because of their gender.
Reagan had pledged during the 1980 campaign to nominate a woman to the court if he was elected.
"The fact is, on the first vacancy, if you weren't a woman no one got into the game in a serious way," he said. "There weren't anybody but women considered virtually from the start. It wasn't any discredit to Dallin. Bork and [now-Justice Antonin] Scalia weren't in the running either because they weren't women."
The newly surfaced memo, written in September 1981 by Hank Habicht, who was a special assistant to the Attorney General, lays out his role in the six-month process of researching and winnowing down a list of candidates.
It was released by the National Archives last week among thousands of pages relating to the nomination of Roberts, who years earlier had been a lawyer at the White House involved in the process.
Other memos written by Roberts describe his role in helping O'Connor prepare for Senate confirmation hearings.
There was some speculation in newspapers at the time that Oaks could be in the running for the 1981 nomination and former Rep. Jim Hansen, then a freshman congressman, said it was fairly well-known in Utah political circles.
Fein said the impact of nominating someone like Oaks rather than O'Connor would have been immense.
O'Connor cast key votes in decisions on affirmative action, abortion, homosexual rights, and religious displays that infuriated conservatives.
"All this prognostication that this would make Reagan a hero in the female community was absurd, and we ended up with a moderate, then a liberal" in O'Connor, said the conservative Fein. "All those kind of wobbly, non-constitutional or extra-constitutional standards never would have seen the light of day, because she was a vital vote in those cases."
In addition to O'Connor and Oaks, the short list included several who were later nominated to the court: Bork, Scalia, and Anthony Kennedy.
Habicht's memo says staff began assembling a list of candidates for the court in March 1981. The top priority was given to five women, including O'Connor. Later, the Attorney General asked him "to research the records of certain other candidates, such as Robert Bork and Dallin Oaks, and to compile a list of other attractive candidates and their backgrounds."
Rex Lee, a former solicitor general and later president of Brigham Young University, was also briefly considered. Had either Lee or Oaks been nominated and confirmed, he would have been the first Mormon on the high court.