Qaraqosh, about 20 kms (13 miles) southeast of Mosul, was emptied of its population in 2014, when Daesh swept through the region.
Iraqi special units earlier this week captured Bartella, a Christian village north of Qaraqosh, Reuters reported.
The offensive that started Monday to capture Mosul. It is expected to become the biggest battle fought in Iraq since the US-led invasion in 2003.