The four U.S. and two Iraqi sources did not specify which security risks had prompted the decision and reports of the potential evacuation pushed up oil prices by more than 4%.
A White House official said U.S. President Donald Trump was aware of the move.
The U.S. embassy in Kuwait said in a statement earlier on Wednesday that it "has not changed its staffing posture and remains fully operational."
Trump has repeatedly threatened to strike Iran if stuttering talks over its nuclear programme fail and in an interview released on Wednesday he said he was growing less confident that Tehran would agree to stop enriching uranium, a key American demand.
The United States has a military presence across the major oil-producing region, with bases in Iraq, Kuwait, Qatar, Bahrain and the United Arab Emirates.
"The State Department is set to have an ordered departure for (the) U.S. embassy in Baghdad. The intent is to do it through commercial means, but the U.S. military is standing by if help is requested," a third U.S. official said.
Another U.S. official said that there was no change in operations at Al Udeid Air Base in Qatar, the largest U.S. military base in the Middle East and that no evacuation order had been issued for employees or families linked to the U.S. embassy in Qatar, which was operating as usual.
Oil futures climbed $3 on reports of the Baghdad evacuation with Brent crude futures at $69.18 a barrel.
Iraq, a rare regional partner of both the United States and its arch regional foe Iran, hosts 2,500 U.S. troops although Tehran-backed armed factions are linked to its security forces.
Israel and Iran also twice exchanged fire last year - the first ever such direct attacks between the region's most entrenched enemies - with missiles and war drones hurtling across Iraqi airspace.
In recent months the United States had deployed more military assets in the Middle East -- including B-2 bombers, which have since been replaced, and extending the deployment of a second aircraft carrier, which has since departed.
A senior Iranian official told Reuters that a military threat has always been part of the United States' negotiation tactics with Iran.
Iran's U.N. mission on Wednesday posted on X: "Threats of 'overwhelming force' won't change facts: Iran is not seeking a nuclear weapon and U.S. militarism only fuels instability."
Kurilla postponed testimony he was due to deliver before U.S. lawmakers on Thursday because of tensions in the Middle East, two other U.S. officials said.
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