The long-awaited pact will allow US forces to stay in Iraq beyond the end of this year, when a UN Security Council mandate enacted after the US-led invasion in 2003 expires.
According to US and Iraqi sources, the draft agreement calls for US soldiers to withdraw from Iraqi cities by the end of next June.
They would remain on bases across the country, however, providing backup support to Iraqi forces until the end of 2011, reports said.
But there are some disagreements over the draft.
Abdul Wahab Al Qassab, an Iraq specialist at the Doha-based think tank the Strategic Studies Centre, said: "There will still be some reservations from a very broad segment of the Iraqi society.
"The only string which [Iraq's government] can play - Iraqi public opinion - is contrary to going into such an agreements with a power which is considered by Iraqis as [an] invader"
Abdul Wahab Al Qassab, Iraq specialist
"[Iraq's government has] only one power. The only string which they can play - the Iraqi public opinion - is contrary to going into such an agreement with a power which is considered by Iraqis as invaders."
Other issues that need to be sorted out include immunity for US troops from Iraqi law and the status of prisoners held by US forces.
"It is an important agreement to allow Iraq and the US to continue co-operation in building a foundation that solidifies the gains made in this country," Rice said.
At present about 144,000 US troops are stationed in Iraq.
Al Jazeera's Tom Ackerman said that with Iraqis facing provincial elections in the next few months, Nuri al-Maliki, Iraq's prime minister, will be facing pressure at home not to concede anything that will affect Iraqi sovereignty and to ensure a firm end date for US troop withdrawal is set.
In May this year, scores of protests against any such deal erupted in Baghdad, led by Muqtada al-Sadr, the Iraqi Shia leader.
Al-Sadr on Thursday denounced both Rice's visit and the proposed pact.
In a statement read by Liwa Smeism, al-Sadr's political adviser, at his office in Najaf, he said: "Today, Condoleezza Rice, the occupation foreign secretary, arrived in Iraq to try to put pressure on the government of Iraq to accept terms dictated by the occupation to sign this ominous treaty."
Any deal would have to be first ratified by the Iraqi parliament and the veto-wielding presidency council.