Should the longest-serving member of the court step aside after 31 years, it would give President Bush the opportunity to pick his first justice. With the GOP winning control of the Senate last month for the new Congress, the president should have an easier time getting his nominee approved.
Rehnquist, a 78-year-old Republican, has not publicly discussed his plans. Traditionally, justices announce retirements in late spring or summer, before the court goes on a summer break.
But many court observers think the political climate, Rehnquist's age and the injury make the time right for a change.
"If I were a betting person, I'd bet all that signals this will be his last term," said Carter Phillips, a Washington lawyer who frequently argues before the high court.
Rehnquist fell at his home in late November and tore a leg tendon. An avid tennis player and walker, he is getting around by wheelchair and crutches while healing from surgery. Rehnquist, known for his tough, no-nonsense demeanor, also has dealt with back pain for years.
But politics, more than health, could determine Rehnquist's future. In a television interview last year, Rehnquist said federal judges typically time their retirements when someone from their party is in the White House.
Rehnquist joined the court in January 1972 after being chosen by President Nixon. He was named chief justice by President Reagan in 1986.
Rehnquist and the other eight justices have been together since 1994, the longest period without a death or retirement since the early 19th century.
"I think it's really time and the chief feels it's time" to retire, said Temple University law professor Mark Rahdert, a former Supreme Court clerk. "He's been waiting for the political winds to blow the right way to ensure his successor is someone who will continue to mold the court toward the conservative philosophy that has animated Chief Justice Rehnquist's career for 30 years now. The political lineups are great."
Rehnquist can leave in 2003 knowing that Mr. Bush would nominate another conservative who will be considered by a Republican-controlled Senate. A retirement is less likely in 2004 because of the politically charged climate of a presidential election year.
The White House has considered possible replacements but won't say much about them. Many of the candidates are likely to be federal judges well known in legal and conservative circles but far from household names. At the head of the list is said to be the man in charge of making the list - Alberto Gonzales, the White House counsel.
Other potential nominees include:
One discussed scenario, if Rehnquist retires, would be Justice Sandra Day O'Connor's elevation to be the first female chief justice and the nomination of Gonzales to replace O'Connor.
That combination could win Mr. Bush political points with women and Hispanics.
Gonzales is a close confidant of the president's and is widely considered his top choice for a court vacancy. But some conservatives, particularly anti-abortionists, are skeptical of Gonzales, who as a Texas Supreme Court justice favored minors' abortion rights. Likewise, some conservatives do not like O'Connor, who backs abortion rights and has a moderate record on some other issues.
O'Connor, 72, is believed to be interested in the chief justice's job. If her age and voting record make her elevation too unappealing to Mr. Bush, O'Connor might retire, too.
Conservatives would prefer to see Mr. Bush elevate Justice Antonin Scalia, though such a move likely would mean a bitter confirmation process because of Scalia's record.
Regardless of whom Mr. Bush nominates, some Democrats may use the confirmation process to vent lingering bitterness from the court's 2000 Bush v. Gore decision, which ensured Mr. Bush's victory over Democrat Al Gore.
That alone would not be enough to scuttle a nomination. But if Mr. Bush picks a strong conservative, some moderate Republicans might side with the Democrats and kill the nomination.
Then there's the possibility that Rehnquist will defy conventional wisdom and stay in the job. Richard Garnett, a former clerk to Rehnquist, sees that as unlikely but possible.
"It is tough to be at the center of the universe, then not be," he said.