U.S. forces under a bilateral security agreement are scheduled to leave Iraq at the end of the year.
Saad Muttalibi, a top lawmaker in Iraqi Prime Minister Nouri al-Maliki's State of Law coalition, told Radio Free Iraq that Washington wants to station as many as 20,000 troops in Iraq beyond the December deadline.
The lawmaker said it was unlikely that Iraq would move to extend the troop deadline, noting any proposal would have to move through the Iraqi Parliament.
Iraqi analyst Assad al-Abadi told the broadcaster, however, that it was in Baghdad's best interest to get an extension.
"Rather than the U.S. applying pressure on Maliki's government to accept a residual U.S. force beyond 2011, it is the latter that should pressure the U.S. to keep some of its forces after Dec. 31 because it is not a good time for the U.S. forces to leave."
Their comments came after a visit to Iraq by U.S. Defense Secretary Robert Gates, who said Washington was taking a wait-and-see approach to a possible extension "because the initiative ultimately has to come from the Iraqis."
Abadi said most of his colleagues agree that a continued U.S. presence would be helpful because of the political situation in Iraq.
Maliki hasn't filled many of the top security posts in his new Cabinet after winning a second term in December.