The Iraqi cabinet sought key changes, including greater legal jurisdiction over US troops and guarantees that US soldiers would not launch attacks on other countries from Iraq.
A reply to the proposed amendments is expected to come within days of the result of the US presidential election.
Sami al-Askari, an MP in the ruling Shia United Iraqi Alliance (UIA), said on Tuesday that the Iraqi negotiators "received positive indications from the Americans regarding the changes proposed in the Sofa [Status of Forces Agreement]."
"But we are yet to receive their response officially," Askari, who is close to the negotiators, told the AFP news agency.
The signing of the pact has been delayed by several months of negotiations between the two sides, as well as bitter divisions in Baghdad and mass protests against the agreement.
The UN mandate for the deployment of foreign troops in Iraq expires on December 31.
On Sunday, Iraq's president dismissed an invitation from Massud Barzani, the leader of the autonomous Kurdish region in the north of Iraq, to the US to set up military bases there if the proposed security pact with Baghdad failed.
Jalal Talabani, himself a Kurd, said Washington could set up bases in the country - even in the Kurdish region - only with Baghdad's approval.
The final draft of the proposed pact must be endorsed by the Iraqi parliament after the amendments are finalised by both Washington and Baghdad.