Mr Bush is expected to deliver a speech next week unveiling a strategy that could include thousands more US troops.
It comes as control of the US Congress passed for the first time in 12 years to the Democrats, who want to apply pressure for a phased Iraq withdrawal.
Mr Bush also spoke by video link to Iraqi Prime Minister Nouri al-Maliki, discussing the security situation in Baghdad and calling for an investigation of the circumstances of Saddam Hussein's execution.
The White House and Pentagon have not confirmed the changes but US media and administration officials have said they will be:
- Adm William Fallon to replace Gen John Abizaid as head of Central Command for Iraq and Afghanistan
- Lt Gen David Petraeus to take over from Gen George Casey as the leading ground commander in Iraq
- US ambassador to Iraq Zalmay Khalilzad to replace John Bolton as US ambassador to the UN
- Ryan Crocker, US ambassador to Pakistan, to replace Mr Khalilzad in Baghdad
On Friday, Mr Bush confirmed he had named retired Vice Admiral and intelligence official Michael McConnell to replace John Negroponte who has been appointed deputy secretary of state.
Adm Fallon is currently the top military commander in the Pacific and, if confirmed, the move will put a navy man in charge of two land wars.
Leading Democrat Senator Daniel Inouye said Adm Fallon was "well educated and respected" and that his nomination would "go flying through" Congress.
A senior White House official said Mr Bush might make the official announcement on Mr Khalilzad as early as Friday.
Mr Khalilzad would have to be confirmed by the Senate, but analysts say he has maintained good relations with the Democrats.
The BBC's Sarah Morris in Washington says the new strategy could include a deployment of 20,000 fresh troops to be stationed mostly in and around Baghdad with the intention of disarming the militia groups there.
But Mr Bush said he needed to hold further consultations before he outlined the strategy.
Some members of the new Congress have been invited to the White House on Friday for discussions, the Associated Press news agency said.
Correspondents say the Democrats, newly installed in power in both houses, will not be supportive of the strategy.
And the new Speaker of the House of Representatives, Nancy Pelosi, called for a plan to start a troop pull-out.
Nancy Pelosi said the US wanted a new direction in Iraq
"It is the responsibility of the president to articulate a new plan for Iraq that ... allows us to responsibly redeploy our troops," she said in her inaugural address.
The BBC's Adam Brookes in Washington says Mrs Pelosi's views appear to represent a growing consensus among Democrats that the US should start scaling down its commitment in Iraq.
But there is no sign that the president will be talking about troop withdrawals, our correspondent says.
In a two-hour teleconference with Mr Maliki on Thursday Mr Bush agreed there should be "sufficient" security forces in Baghdad, the White House said.
The US president said he had sought and received assurances from Mr Maliki that he had the will to do what was necessary to protect Iraqis against increasing sectarian violence.
Mr Bush said: "One thing is for certain: I will want to make sure that the mission is clear and specific and can be accomplished."
The president also said he wished the execution of ex-Iraqi leader Saddam Hussein had been more dignified and that there should be a "full investigation".
However, he said Saddam Hussein had been given justice that "the thousands of people he killed had not".