The US still has 130,000 troops in Iraq but they are now working in support of Iraqi government forces rather than taking a lead role in providing security, under the Status of Forces Agreement (Sofa),
Obama is expected to suggest ways to address differences between Iraq's Shia, Sunni and Kurdish communities, the US official said.
Washington "will not dictate the solutions to al-Maliki" but will offer assistance to Iraqi "efforts to address political issues and build national unity," the official said.
Al-Maliki met Ban Ki-moon, the UN secretary-general, in New York earlier on Wednesday in an effort to ease UN sanctions imposed on Iraq after its invasion of Kuwait in 1990.
The Iraqi prime minister then held talks with envoys of the five permanent members
of the UN Security Council - Britain, China, France, Russia and the United States.
"We were able to clarify... that Iraq does not appear to be a threat to the international community any more," al-Maliki told reporters after the meeting, saying that sanctions are "no longer required".