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 Adel 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 to send a "clear and unmistakeable" message to Iran.
National Security Advisor John Bolton said the deployment was in response to a "number of troubling and escalatory indications and warnings," but did not elaborate.
"The United States is not seeking war with the Iranian regime, but we are fully prepared to respond to any attack, whether by proxy, the Islamic Revolutionary Guard Corps, or regular Iranian forces," he said.
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.
But in response to a question about threats from Iran or its proxies on US forces in Iraq, the top US diplomat mentioned both Iraq and Jordan.
"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.
