The source, speaking on condition of anonymity because of the high security nature of the visit, said Pompeo was set to meet Iraqi Prime Minister Adil Abdel Mahdi.
The visit comes two days after the US announced it was dispatching an aircraft carrier strike group and bomber task force to the Middle East.
Pompeo had been en route to Germany but suddenly cancelled the trip due to "pressing issues," the State Department said, without elaborating where he was heading.
"As Secretary of State I have a responsibility to keep the officers that work for me safe each and every day all around the world. That includes in Erbil and Baghdad, in our facilities in Amman, all around the Middle East," he said.
"And so any time we receive threat reporting, things that raise concerns, we do everything... that we can to make sure that those planned or contemplated attacks don't take place, and to make sure that we've got the right security posture," he said.
Pompeo had been traveling from Finland, where he had attended a meeting of the Arctic Council.
He was due to meet both Chancellor Angela Merkel and Foreign Minister Heiko Maas later Tuesday in Germany.
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