Goss will be named by Bush Friday to succeed George Tenet, who announced his resignation June 3, the official said.
However, White House Communications Director Dan Bartlett said, "The president has not made a decision and there's more than one candidate," the Associated Press reported.
Goss had been leading an investigation into intelligence failures leading up to the Sept. 11, 2001, terrorist attacks.
Goss previously had announced his intention to retire at the end of this term, his eighth serving in the House.
House Minority Leader Nancy Pelosi, D-Calif., told reporters Thursday she would probably not support Goss if he were selected to run the CIA.
Pelosi cited what she described as partisan behavior during debate on intelligence reauthorization.