The report said the Israeli planes participating in the drills include F-15, F-16, F-18 and F-22 fighter jets. It said they have conducted weeklong exercises,flying mainly at night.
Press TV said its report was based on information received from a source close to Moqtada al-Sadr's group in Iraq.
Sadr is considered to be one of the most influential religious political figures in Iraq but holds no official title. He has repeatedly called for the immediate withdrawal of U.S.-led coalition troops and U.N. forces deployed in Iraq.
The air drills are being conducted in collaboration with the U.S. military, the report said. It said Iraq was not informed of the exercises.
The U.S. maintains a number of military bases in Iraq and the government in Baghdad is not involved in any military activities occurring there, the report said.
There was no official comment on the report by Israeli government or military officials.
Last month, Brig. Gen Mohammed Ali Safari, the commander of the Revolutionary Guards, declared Israeli and American military bases in the Middle East are within range of Iran's missiles.
"Although we are capable of increasing the range of our missiles, we don't think it would be necessary because today our extra-regional enemy -- the Zionist regime of [Israel] -- is within the range of our missiles," he told the Fars news agency.
"As for the American forces -- if they were to back Israeli threats -- they would be closer to us than them [Israel] and they would be within the range of our firepower as well," he said.