Washington's favorite game — name the next Cabinet member — is underway and a bevy of well-known and well-liked former and current officials are being talked up as possible replacements for outgoing Attorney General Alberto Gonzales.

Most frequently named — in part because of his proximity to the post — is Solicitor General Paul Clement.

President Bush said Monday that Clement will serve as acting attorney general after Gonzales leaves on Sept. 16. Clement has solid conservative credentials and is highly regarded around Washington.

"Paul is one of the finest lawyers in America. As solicitor general, Paul has a representation of fairness and earned the respect and confidence of the entire Justice Department," Bush said during remarks on Gonzales' resignation.

Theodore Olsen, a former solicitor general who is well-respected on Capitol Hill, also has been put on the list of possibilities.

"Ted Olsen would be great. ... I think (current White House counsel) Fred Fielding would be another great name," said former deputy assistant to President Bush Brad Blackman, adding that it's important the White House fill the slot quickly.

"I think the best choice would be somebody who comes from outside the administration who would have an easy time getting confirmed without the quote-unquote baggage of having served," he said.

Other possible successors include Asa Hutchinson, the former head of the Drug Enforcement Administration, and former Deputy Attorney General Larry Thompson, who is frequently named as a potential candidate to fill an array of vacancies. Current Homeland Security Secretary Michael Chertoff, a former federal prosecutor, assistant attorney general and federal judge has also been suggested, but his tenure as head of the DHS is open to attack.

"Let's say it's Michael Chertoff. Undoubtedly, the Democrats are going to revisit (Hurricane) Katrina" recovery efforts, said University of Virginia Center for Politics head Larry Sabato. "They're going to use the nomination hearings for attorney general to re-analyze something that happened two years ago in a completely different realm. But that's politics."

Already, Sen. Chuck Schumer, who led the battle against Gonzales, has said he's not keen on Chertoff as the choice.

"I would say there are a lot of questions about Michael Chertoff that will have to be answered. I wouldn't say yes; I wouldn't say no. It's an open book. It's possible, but it's hardly a slam dunk. There are some names who could be a slam dunk," said Schumer, D-N.Y.

But Sen. Arlen Specter, the top Republican on the Senate Judiciary Committee, said Chertoff would be a top-notch choice.

"First-rate prospect. Very, very able. A U.S. attorney. He was a 3rd Circuit judge. He's done an excellent job at Homeland Security. ... I'd be prepared to give him an 'A' rating." he said.

Adding that the candidate has to be "someone with very solid professional qualifications, an experienced lawyer," Specter said that "a senator might be just the ticket," in part because of the Judiciary Committee's familiarity with such a nominee. He excluded his own name from consideration after prodding by reporters.

Bush probably will want to avoid contentious hearings on Capitol Hill following the departure of Gonzales, his longtime friend and ally who Bush said was ousted because of Democratic bloodlust.

"After months of unfair treatment that has created a harmful distraction at the Justice Department, Judge Gonzales decided to resign his position and I accepted his decision," Bush said, reeling off a long list of policies Gonzales helped form as Bush's senior counsel at the White House and at the Justice Department.

"It is sad that we live in a time when a talented and honorable person like Alberto Gonzales is impeded from doing important work because his good name was dragged through the mud for political reasons."

Already, Senate Judiciary Committee Chairman Patrick Leahy indicated that just because Gonzales is out doesn't mean the panel will stop investigating possible political breaches at the Justice Department.

But Weekly Standard Editor Fred Barnes, a FOX News contributor, said the president also needs to nominate someone who can compel Congress to support elements of a warrantless surveillance program and terror suspect interrogation rules.

"My candidate would be Larry Silverman, the appeals court judge, who was very tough, very strong, very smart, and very credible," Barnes said.

Schumer said he was under "no illusions" that the president will name a Democrat, but the nominee must be someone who Democrats are confident "will put the rule of law above political considerations."

He urged the administration to consult Democrats before naming a replacement to serve out the remaining 17 months of Bush's term.

"We're not looking for confrontation. The ideal situation would be for the White House to come and talk to us and say, 'Here are some possibilities. What do you think?'" Schumer said.

FOX News' Bret Baier and Trish Turner contributed to this report.