According to the report, the market is called "Spoils of the Nazarenes," and sells electronic devices such as televisions, refrigerators and microwave ovens, in addition to furniture and artwork.
Mosul is one of Iraq's largest cities, which was overrun by IS last June. IS drove Assyrian Christians out of Mosul, where now only Sunni Arabs remain.
The jihadi movement declared its cross-border caliphate last year after seizing territory in eastern Syria and west and northern Iraq. Reuters contributed to this report