"My desire is to get this process moving so that someone will be confirmed, whoever he or she is, will be confirmed by October," Mr. Bush said at a joint news conference with India's Prime Minister Manmohan Singh.
Mr. Bush indicated that he is already so familiar with some of the candidates that he does not need to interview them for the first high court vacancy in 11 years.
"I've got some people, perhaps in contention, that I've already spent time with, that I know. In other words, I'm familiar with some people that are being speculated about in the press. And so I don't need to interview those. But of course I'm going to take a very thorough approach," Mr. Bush said.
O'Connor announced her plans July 1 to step down once the Senate had confirmed a nominee.
Mr. Bush poked fun at the rampant Washington speculation that he was close to naming his Supreme Court nominee.
"Well, thank you for telling me where I am in the process. I appreciate that," he said in response to a question.
The president said he had consulted with members of the Senate and will continue to do so. He said part of that contact was to determine the Senate schedule to "get somebody in place by the October session."
The candidates mentioned most often are federal appeals court judges: Samuel Alito, Emilio Garza, J. Michael Luttig, John Roberts Jr., Michael McConnell and J. Harvie Wilkinson III. Luttig and Wilkinson sit on the 4th U.S. Circuit of Appeals in Richmond, Va.
Attorney General Alberto Gonzales has also been mentioned as a potential pick, although some conservatives have criticized the former Texas judge on abortion and affirmative action decisions. Women jurists also mentioned include Edith Hollan Jones and Edith Clement, both on the New Orleans-based 5th Circuit Court of Appeals.
On Sunday, Sen. Arlen Specter, R-Pa., chairman of the Senate Judiciary Committee, said that he would like to see a moderate in the tradition of O'Connor and perhaps someone with experience in politics.
Specter, who declined to recommend a specific candidate because of his role as chairman, also said he would like to see a nominee who has experience outside the judiciary.