US officials also said the Bush administration was considering allowing all countries to bid on the next round of contracts.
The decision would signal an abandonment of Washington's earlier stand ruling out for bidding countries that opposed the Iraq war.
The officials however said they did not expect an announcement about French firms for several weeks, adding that something could still derail the emerging consensus within the administration.
Speculations of a major policy rethink on Iraqi contracts have gained momentum after Bush announced on Tuesday that Canadian firms would be allowed to bid.
Administration officials have since been saying that others, including companies from Germany, Russia, which like France opposed the war, could also be included.
"I have heard people backpedaling all over the government on this," one official said.
"I have heard people backpedaling all over the government on this"
"We have got time. We have basically got a couple of weeks before the next round of tenders go out," he said.
Bush effectively punished war opponents like Canada, France, Germany and Russia a month ago by barring them from bidding on the lucrative reconstruction projects.
He said he was restricting contract bids to countries that risked lives in Iraq.
US officials have since privately acknowledged that the decision to bar some countries was a public relations disaster and a self-inflicted wound and they have been looking for a way to repair the diplomatic damage.
The shift on Canada followed an acknowledgment by US officials that they wanted to put the bitter Iraq war debate behind them and patch up relations.