Mr Bush is expected to opt for military man General Michael Hayden to head up the US intelligence agency, which has been embroiled in controversy in recent years.
Leading Republicans and Democrats may try to block the appointment leading to a possible congressional showdown with the White House.
Both Republican and opposition Democratic legislators voiced concern about putting a military officer in charge of the agency instead of a civilian, and cited General Hayden's support for a controversial domestic spying program as a worry.
At issue is whether a career military man like air force General Michael Hayden should head the agency at this time.
"Bottom line, I do believe he's the wrong person, the wrong place, at the wrong time," said Pete Hoekstra, a Republican congressman who chairs the House Intelligence Committee.
"We should not have a military person leading a civilian agency at this time. Regardless of how good Mike is, putting a general in charge is going to send the wrong signal," said Mr Hoekstra, who added that relations between the CIA and Department of Defence had been strained.
"The danger of having the military take over intelligence is that the military has a very different perspective on the world," he said.
Republican senator Pat Roberts, chairman of the Senate Intelligence Committee, said General Hayden could ease those concerns by resigning as an Air Force general and naming civilians as his deputies.
Still, Mr Roberts, who praised the general as an expert on intelligence, would not say whether he would vote for General Hayden's nomination. His committee must endorse the nomination and send it to the full Senate for approval.
"I'm not in a position to say that I am for General Hayden and will vote for him," he told CNN.
Democratic Senator Dianne Feinstein expressed concern about military control of most intelligence matters.
"You can't have the military, I think, control most of the major aspects of intelligence," she told America's ABC television.
Lawmakers expect to grill General Hayden, now the principal deputy director of national intelligence, over the domestic eavesdropping program, which he oversaw during his time as director of the National Security Agency.
"I have some very pointed questions," Republican Senator Arlen Specter, head of the Senate Judiciary Committee, told Fox News.
"I want to know what the program is. We cannot judge its constitutionality without knowing what the program is."
Former CIA head Mr Goss was reportedly forced out due to disappointment over his leadership of the CIA.
He was appointed less than two years ago to reform an agency under fire over the September 11, 2001 terrorist attacks and pre-war intelligence on Iraq.
But Mr Goss upset the US spy establishment when he named some of his congressional allies to top jobs and used strongarm tactics in a bid to reform agency.
Sources also suggested Director of National Intelligence, John Negroponte, had been sharply critical of Mr Goss.
They say complaints by the president's Foreign Intelligence Advisory Board pushed Mr Goss out the door after news of an investigation into his Number 3 aide at the CIA that involves prostitution and cronyism.
Vice President Dick Cheney praised Mr Goss as "a very able and talented public servant" who took the CIA job at a difficult time and did a "reasonably good job".