British soldiers could be sent to support American forces in some of Iraq's most volatile areas.
Most British soldiers are currently based in southern Iraq
Senior British military sources say the US has asked British troops to fill in behind American soldiers, who are being sent elsewhere.
It is believed UK forces could be sent from Basra, in southern Iraq, to an area south of Baghdad.
BBC defence correspondent Paul Adams said they would be under US command, which might cause controversy.
No decision made
The Ministry of Defence confirmed discussions were taking place, but said no decision had been made.
The proposal sparked warnings from opposition parties.
Tory leader Michael Howard called for a statement from the government.
He said: "If it's the case that British troops are to be moved out of area, it's vital that a statement is made in Parliament at the earliest possible opportunity so that we can ask the relevant questions."
Liberal Democrat defence spokesman Paul Keetch warned against placing British forces under US command.
He said: "British forces should remain under direct British control within the British sector. Any change to this basic command structure should be brought before the House of Commons.
"With the public disquiet about ongoing operations in Iraq, placing British forces under direct US control would not be supported by the British people."
The deployment, which would involve up to 650 personnel, is expected to last "a few weeks", the BBC was told.
It would allow US forces to be sent from Baghdad to join those involved in operations in the insurgent stronghold of Fallujah.
One option being considered would involve Scottish troops from the Black Watch Regiment extending their tour of duty in southern Iraq by a short period.
If this option is pursued, the plan would be to have the regiment home in time for Christmas.
Speculation that Black Watch could be redeployed emerged from families of its soldiers.
Troops are currently acting as the reserve force in the southern city of Basra, and their relatives say they were told they would not be returning home next month as planned.
A MoD spokesman said no decision had been taken to extend their current tour: "Discussions are continuing as these things are always discussed. But if these discussions lead to a decision it will be announced in the normal way."
One military source told Paul Adams the request to move troops was a matter of being a "good ally" to the US, and it was no good "sitting pretty" in the south in large numbers when the Americans were doing all the difficult work elsewhere.
The source added the move was seen as posing no significant additional dangers to those already faced by British forces in the country's south.
Southern Iraq has been comparatively peaceful
The movement of troops, if agreed to, would not necessarily add to the numbers of British soldiers stationed in Iraq.
A separate decision could be taken to boost numbers ahead of the elections, but a decision on this has also not been made.