The US approach comes at a time when bilateral relations between the two NATO countries are at their lowest ebb in years.
Local press reports suggest the scheme may have been conceived during a visit by two senior US generals to Ankara on Friday.
The US administration is searching for allies to share some of the burden of peacekeeping and reconstruction in Iraq. Still, many nations, including India, France and Germany, said they were only prepared to commit troops if the UN was given overall responsibility for running operations in the country.
Hurriyet, one of Turkey’s leading newspapers, reported the US delegation asked Ankara to send 10,000 troops to the war-ravaged country.
Relations between Washington and Turkey soured when in March Turkey refused to allow US-led forces to open a northern front against Iraq from its territory.
The arrest of 11 Turkish soldiers in Iraq by US soldiers earlier this month further angered Turkey’s government. The US accused the soldiers of planning to assassinate a prominent local Kurdish official.