The Post says White House lawyer Brett M. Kavanaugh will be nominated for an opening on the U.S. Court of Appeals for the District of Columbia, which is considered the second most powerful court in the nation, after the U.S. Supreme Court.
The report comes a day after the White House rejected an offer from Senate Democrats to meet to discuss ways to avoid a nasty partisan fight over potential Supreme Court nominees.
Kavanagh, 38, worked for Starr from 1994 to 1998 and was involved in many of the Clinton administration's legal controversies. He worked on the Monica Lewinsky investigation and wrote the section of the Starr report that outlined possible legal grounds or President Clinton's impeachment.
He also worked with Starr on the successful effort to force White House lawyers to release notes of conversations with Hillary Rodham Clinton relating to the suicide of deputy White House counsel Vincent Foster.
As a White House lawyer, Kavanaugh has played a key role in selecting Mr. Bush's judicial nominees.
The Post says Kavanaugh is already undergoing an FBI background check in preparation for the nomination, which is not expected to be announced right away.
On Wednesday, the White House turned down a suggestion by Senate Minority Leader Tom Daschle that Mr. Bush meet with Democrats before filling any Supreme Court vacancies to avoid a potentially bruising confirmation fight.
"Unless and until there is a vacancy, this is idle chit chat," said Mr. Bush spokesman Ari Fleischer.
Should there be such a vacancy, White House counsel Alberto Gonzales will be happy to meet with senators to discuss the process, Fleischer said.
"But the Constitution is clear, and the Constitution will be followed," Fleischer said, referring to the president's constitutional right to fill Supreme Court vacancies.
There has been rising speculation that Mr. Bush may soon have an opportunity to make his first Supreme Court nomination, possibly even two.
June traditionally is a time for retirement announcements on the court — so that the Senate can hold confirmation hearings before the court reconvenes in October. The most likely prospects for resignation are Chief Justice William H. Rehnquist, 78, and Justice Sandra Day O'Connor, 73.
Both parties are bracing for a potentially bruising confirmation fight, given close GOP control over the Senate and the fact that Mr. Bush's court selections could make a huge difference on many crucial social issues for years to come — including abortion, the death penalty and racial questions.
Daschle on Tuesday asked the president to call a meeting with leaders in both parties to talk about ways to avoid such a battle over a possible Supreme Court nomination.
"Should you be willing to convene a meeting of Senate leaders from both parties to begin a bipartisan process of consultation, I stand ready to participate in good faith in such a process," Daschle said in a letter to the White House.
But Fleischer told reporters Wednesday that Daschle and other Senate Democrats had "come up with a novel new approach of how the Constitution guides the appointment process."
Gonzales, in a letter Tuesday to Senate leaders, said that Mr. Bush would nominate "an individual of high integrity, intellect and experience" if a vacancy comes open.
"The Senate will have an opportunity to assess the president's nominee and exercise its constitutional responsibility to vote up or down on the nominee," Gonzales wrote, also offering to meet with senators himself.
Ranit Schmelzer, a spokeswoman for Daschle, expressed disappointment Wednesday at Fleischer's comments apparently ruling out any meeting between Mr. Bush and Democrats on the issue.
She said no one was questioning Mr. Bush's authority to act on his own in filling federal judicial vacancies.
"We're just asking for a little civil discourse on this, bipartisan discourse," she said.
But Fleischer said that naming someone to the Supreme Court is not the same as discussing legislation with lawmakers, which Mr. Bush does regularly.
"There's a significant difference between the naming of an individual and a piece of legislation that has a hundred moving parts to it," he said.
"We always welcome thoughts," Fleischer said, but, he added, "No one wants to suggest that the Constitution be altered."
In any event, he added, "There's not even a vacancy."
Despite the widespread speculation, neither Rehnquist nor O'Connor have given any public clues that retirement announcements were imminent.