The Turkish press said on Thursday the United States wanted Ankara to send up to 10,000 troops as soon as possible, following Tuesday's vote in the Turkish parliament in favour of deployment.
US officials, already embroiled in a row with Iraq's Governing Council which does not want any Turkish troops, want to avoid any protracted bargaining with Turkey.
But Turkey's Hurriyet daily said Washington had opposed a Turkish request to station forces between Baghdad and a Kurdish-controlled enclave in Iraq's north, fearing this would upset the Iraqi Kurds.
It said US military officials asked the Turkish military in a closed-door meeting on Wednesday to deploy its forces west of the Iraqi capital, towards the border with Syria and Jordan, and further from the enclave.
Kurds on the US-appointed Iraqi Governing Council suspect Ankara may work to obstruct any further autonomy for their enclave, particularly if Turkish soldiers are deployed nearby.
The Council opposes the presence in Iraq of soldiers from any neighbouring country.
Council members say the body plans to make a formal announcement on its stance, but this has been repeatedly delayed.
Iraqi Governing Council does not
want Turkish troops in Iraq
Turkey says Kurdish concerns are unfounded and insists it is sending peacekeepers to help stabilise Iraq and help with reconstruction efforts.
But Ankara fears any moves by Iraqi Kurds for independence from Baghdad could spark unrest in its own southeast, where it has fought a decades-long war against the Kurdistan Workers' Party (PKK), at the cost of more than 30,000 lives.
Ankara already stations thousands of troops just inside northern Iraq in a controversial deployment it says is necessary to prevent PKK rebels returning to Turkey to launch new attacks.
The PKK recently called off a unilateral ceasefire after five years.