The authorities in Baghdad say they are preparing for an exodus of thousands of people from eastern parts of the city.
Fighting between government and US troops on one side, and Shia militia on the other, has intensified recently.
Two football stadiums are on stand-by to receive residents from two neighbourhoods in the Sadr City area.
The government has warned of an imminent push to clear the areas of members of the Mehdi Army, loyal to the anti-American cleric, Moqtada Sadr.
In the last seven weeks around 1,000 people have died, and more than 2,500 others have been injured, most of them civilians.
The fighting so far in Sadr City has been fierce - street to street, and house to house.
Iraqi Prime Minister Nouri Maliki is showing a determination to disarm the country's Shia militia groups - particularly the Mehdi Army - that he has never displayed before.
However, Iraqi army operations, backed by US ground and air support, have so far failed to overwhelm the Shia militiamen, who are still responding with roadside bombs, sniper fire, mortars and rockets.
The government has distributed leaflets in two key districts of Sadr City, warning people to leave.
The speculation is that government forces are preparing for a big push into eastern Baghdad to end the current fighting once and for all.
Shortages of water and medical supplies have already made life inside Sadr City extremely difficult.