Others say he may not want to be chief justice because the position would reduce his freedom to skewer his colleagues in sharply worded dissents while championing his vision of constitutional "originalism."
"I think it would mute his voice," says Todd Gaziano, director of the Heritage Foundation's Center for Legal and Judicial Studies in Washington.
Scalia is the best known among the six or seven others said to be on Mr. Bush's Supreme Court shortlist. In his 19 years as an associate justice, Scalia has become the nation's leading proponent of an originalist approach to constitutional law.
In his view, judges exceed their authority when they impose their own policy preferences by expanding constitutional rights that never existed in the original document. He says by looking to the text of the Constitution as it was originally written, judicial discretion can be minimized and true constitutional freedoms better preserved.
It is an approach that is increasingly resonating with many conservatives upset over what they view as unrestrained activism by US judges - including some jurists appointed by Republican presidents.
Still, there are several unknowns. Chief Justice Rehnquist, who is undergoing cancer treatments, has given no hint of an intention to step down. And although Bush has cited Scalia and Justice Thomas as the type of judges he would seek to appoint to the federal bench, it remains unclear whether his admiration will translate into a chief-justice nomination.
There are also potential strategic considerations. By promoting a chief justice from within the court rather than simply naming a single nominee from outside, the White House would face two confirmation battles, rather than one.
Perhaps Scalia's biggest advantage - and disadvantage - is his extensive public record of nearly two decades of opinions, famous dissents, and law-school speeches. "With Justice Scalia, you know what you are going to get, so there isn't a huge mystery there," says Michael Gerhardt, a constitutional law professor at William and Mary School of Law in Williamsburg, Va.
Because he has become such a high-profile target, a Scalia confirmation hearing would quickly transform into a national debate over the role of judges in interpreting the Constitution.