The Bush administration is planning to send some 21,000 troops into Iraq in addition to the 138,000 already there, in a last-ditch effort to restore security in the country.
Josh Rushing, Al Jazeera's military analyst, said the British move could cause problems for the Bush administration which is trying to argue for an escalation in US troops in Iraq when its main ally seems to be pulling out.
He said Blair's reported announcement would make the argument in Washington for what is being called a "troop surge" much more difficult to maintain.
"What was once called the coalition of the willing, was really just the US and Britain – and now Britain seem to be pulling out," he said.
Britain currently has about 7,100 troops in Iraq, most of them based around the southern city of Basra.
The British force is the second-largest foreign contingent of soldiers after that of the United States, which has more than 140,000 troops in Iraq.
Gordon Johndroe, a spokesman for the Bush's administration's National Security Council, said Blair had informed Bush of his plans to withdraw troops on Tuesday morning.
He suggested that Blair's move was a signal of increasing stability in Iraq.
"President Bush sees this as a sign of success and what is possible for us once we help the Iraqis deal with the sectarian violence in Baghdad," Johndroe said.
"The president is grateful for the support of the British Forces in the past and into the future.
"While the United Kingdom is maintaining a robust force in southern Iraq, we're pleased that conditions in Basra have improved sufficiently that they are able to transition more control to the Iraqis."
He added: "The United States shares the same goal of turning responsibility over to the Iraqi Security Forces and reducing the number of American troops in Iraq."
Blair had late last month rejected calls for a complete pull-out of British troops saying the plan was "deeply irresponsible".
A total of 132 British soldiers have died since the start of the US-led invasion in March 2003, according to an Agence France Press count based on Pentagon figures.
Blair's office has made no comment on the reports saying any announcement would first be made in the British parliament.
Blair has said he will step down as Britain's prime minister by September after 10 years in power.