Eight months since American troops withdrew from Iraq, Baghdad has signalled a readiness to bolster military ties with the US, America's top general said ahead of a visit to the country.

General Martin Dempsey, chairman of the US Joint Chiefs of Staff, who is due to fly to Iraq this week after talks in Afghanistan, will be the highest-ranking American to travel there since the end of the troubled US military mission in the country.

Speaking to reporters late Sunday aboard his plane en route to Afghanistan, Dempsey acknowledged arch-foe Iran was trying to expand its influence in Iraq but said the Baghdad leadership wanted to build up relations with the American military.

"I believe they've concluded that they missed a window of opportunity to establish a more normal relationship with us," said Dempsey, referring to discussions with Iraqi defence chiefs.

"I don't mean to say we're coming back to Iraq," he said.

"I think they recognise their capabilities may require yet more additional development and I think they're reaching out to us to see if we can help them with that."

The Iraqi defence minister and military chief have both inquired about staging drills with the US military, organising training for Iraqi officers and other "security cooperation", Dempsey said.

His visit coincides with growing concern in Washington that Iran may be funnelling supplies to the regime in Syria through Iraq.

Dempsey did not comment directly on the reports but said: "I will of course express our concern about Iranian influence in Syria."

The general also said he could not confirm reports that Tehran is circumventing economic sanctions by illegally operating in Iraqi financial markets, gaining access to much-needed US currency.

"I've read the reports. I've queried the system for as much intelligence as I can gain," he said.

The general predicted that Iran would seek to strengthen its presence in Iraq if its allies in Syria fall from power.

"My judgment would be that if their position erodes in Syria, my guess is they would seek to increase their influence in Iraq. Strategically, they will seek some other outlet."