Mosul fell to IS in June 2014 and has since been run by the militants.
Tens of thousands of Christians were forced to flee after being told they would be killed if they did not convert to Islam or pay a hefty tax.
Coalition forces are supporting the Iraqi military's attempts to take back the city, which lies about 250 miles north of Baghdad.
Air strikes in recent days have seen the country's government take control of towns and villages around Mosul leading to hopes a complete recapture could be just weeks away.
Martin, a Christian youth leader forced to flee has been urging believers to pray.
"Of course we want to go back to our houses, unlock the doors and start rebuilding," he told Open Doors. "Now we are just praying it will be liberated soon."
He added: "Jesus tells us to forgive, not to forget.
"We can stand up for our rights and ask to be respected as Christians in the Iraqi society, ask for a liberation of our village and the rest of the Nineveh Plain area and Mosul."
While the Syrian city of Raqqa is considered the Islamic State's de facto capital, Mosul is the largest city under its control.