Iraqi forces have had control of the eastern part of the city, which is divided by the Tigris River, since January.
The leaflets say Iraqi forces are making advancements to the western side and "provide guidance and recommendations" for citizens ahead of the offensive, according to a statement from the Iraqi Joint Operations Command (JOC).
The leaflets also warn ISIS members to "lay down their weapons and surrender before they face their inevitable fate at the hands of our heroic forces," the statement said.
As many as 800,000 civilians live in western Mosul, according to the United Nations
. It said UN humanitarian agencies in Iraq are preparing to assist civilians caught in the fighting.
"The situation is distressing," said Lise Grande, the UN humanitarian coordinator for Iraq. "People, right now, are in trouble. We are hearing reports of parents struggling to feed their children and to heat their homes."
Iraqi F-16 fighter jets carried out airstrikes Friday and Saturday in western Mosul targeting ISIS headquarters and communications positions, according to the Iraqi military.
The airstrikes "destroyed a number of ISIS' command-and-control centers, inflicting heavy losses to them and their equipment," the army said.
The offensive to retake Mosul from ISIS's brutal rule began in October 2016 with a push by the Iraqi army, counter-terrorism forces, federal police and Kurdish Peshmerga fighters.
ISIS seized Mosul, Iraq's second largest city, in 2014 and it is the militant group's last major stronghold in the country.