The city has been under ISIL control since the militants took over in June last year, sweeping through most of Iraq's Sunni Muslim provinces towards Baghdad.
The government has promised a military offensive to retake Mosul but progress has been slow, in part because of ISIL gains elsewhere. In May, they drove the army out of the city of Ramadi, capital of the western province of Anbar.
"The solution, with God's help, is close," said the leaflets, which were issued in the name of the Iraqi army and were dropped over Mosul on Friday. "Your armed forces are at the gate, cooperate with them."
Despite that promise, there has been no sign of an imminent military operation against ISIL in Mosul.
The leaflets also promised a new radio station, Mosul FM, would start broadcasting soon and urged residents to carry a small radio with them at all times to receive instructions about the battle for Mosul, Reuters reported.
Mosul residents contacted by telephone said ISIL fighters were deployed in the areas of the city where the leaflets were dropped, telling passers-by to stay away.