Lieutenant-Colonel Christopher Garver, a US military spokesman in Baghdad, said he could not confirm the reports but officials were checking the information.
"We have heard about this ... but I cannot confirm anything at this stage," Garver said.
Rash of crashes
A Chinook has two crew members and can carry up to 55 passengers. They are used widely to transport troops and cargo around Iraq.
The reports came five days after a US Army helicopter crashed in a hail of gunfire north of Baghdad, police and witnesses said - the fourth helicopter lost in Iraq in a two-week span.
US command said two crew members were killed in that crash.
The US military said on Sunday it was adjusting its tactics in Iraq after four helicopters were shot down in recent weeks.
Those helicopters were shot down in four separate incidents in which 21 US servicemen and private security contractors were killed.