"We have not made a decision yet, but if we decide to send troops, their number would be about 10,000," said Abd Allah Gul in a newspaper interview published on Saturday.
But he also made it clear Turkey was concerned by a resurgence of attacks by the separatist Kurdistan Workers' Party.
Turkish authorities believe around 5000 fighters from the party, now known as Kadek, have sought refuge in the mountains that straddle Turkey's border with Iraq.
Three Kurdish guerrillas and two Turkish soldiers were killed during a fierce gun battle in Turkey's troubled southeast on Friday, said Turkish military sources.
Another seven Turkish soldiers were injured in the firefight some 80km from the border with Iraq.
We're not Iraq's enemy
Gul said Turkish soldiers would not be as exposed to attacks in Iraq as US troops, which have been subjected to daily, often deadly attacks over the past few weeks.
"To the Iraqi people, a Turkish soldier is just not like a US one, we are not an enemy," he told the tabloid Star newspaper.
Gul was speaking after a Friday meeting of the Turkey's National Security Council, where the government and military chiefs stressed the need to stabilise Iraq, without explicitly calling for a Turkish contingent to be sent there.
The issue will also be discussed at a cabinet meeting on Monday, with a vote in parliament to take place by mid-September, according to some press reports.
In early March, the Turkish parliament triggered Washington's anger by rejecting government plans to allow US troops to invade northern Iraq from Turkey.
A decision to send Turkish troops to Iraq is seen as a possible way of mending fences with the US administration, as well as giving Ankara a say in its troubled neighbour's political future.