The report on Saturday finally gave a date after months of delays in the face of domestic opposition.
A Defence Ministry official told Reuters the timing of the troop dispatch was likely to be fixed next week.
The government has pledged to send 3000 soldiers to northern Iraq to complement 650 South Korean army medics and engineers who have already been in Iraq for a year.
If the pledged forces are sent, South Korea will have the third largest military contingent in Iraq, after the United States and Britain.
The government has said it will proceed despite small protests and opposition from some members of parliament.
"(The government) is seeking to send 1000 troops in a divisional headquarters and another 1000 in a brigade between July and August," the JoongAng Ilbo daily quoted a senior Defence Ministry official as saying.
Koreans could soon be the third
biggest foreign force in Iraq
The deployment of the remainder of the troops would be decided after observing the situation in Iraq, he said.
"We have not made an official announcement on the time-frame and other details, and expect the decision would be made around next week," Shin Kyung-ja, a Defence Ministry spokeswoman said.
A committee of security-related ministers is expected to hold another meeting next week to give a final nod to the plan.