President Bush is very close to naming his pick to succeed Attorney General Alberto Gonzales, an announcement that could come as early as Wednesday, administration and congressional sources told FOX News on Tuesday.

Under fire from Congress over the dismissal of nine U.S. Attorneys and questions over his truthfulness in testimony, Gonzales announced his departure on Aug. 27, making Sept. 16 his last day on the job.

Until a new attorney general is confirmed by the Senate, Gonzales' shoes will be filled by Solicitor General Paul Clement. Clement is the second-highest ranking official confirmed by the Senate in the Justice Department.

Sen. John Kyl, R-Ariz., a Judiciary Committee member, said he asked Vice President Dick Cheney on Tuesday during weekly policy lunches what the schedule is for a nominee, and Cheney replied, "very close."

Several names have been floated as possible replacements, including Clement's, but it is a previous solicitor general whose name is rising as the apparent favorite: Theodore Olson. Others suggestions include former Deputy Attorney General Larry Thompson and former Deputy Attorney General George Terwilliger III.

A House Judiciary Committee source close to the discussions told FOX News that Sen. Orrin Hatch, R-Utah, also is being strongly considered.

Politico.com reported Monday said the list of finalists also includes Michael Mukasey, a New York attorney and former chief judge for the U.S. District Court of the Southern District of New York; and Laurence H. Silberman, who sits on the U.S. Court of Appeals for the District of Columbia Circuit.

And Sen. Charles Schumer, D-N.Y., also on the Judiciary Committee, told reporters that he was assured last Friday by White House counsel Fred Fielding that when the administration was "very close (to a decision) he'd call me again. He hasn't yet."