"All are doing well," the official said.
The kidnappings came a day after the Mosul consulate said fighters from the powerful jihadist group the Islamic State of Iraq and the Levant (ISIL) seized 28 Turkish truck drivers.
In a spectacular blow to the Shiite-led government in Iraq, jihadists spearheaded by ISIL on Tuesday seized Mosul, its surrounding region of Nineveh and areas of Kirkuk and Salaheddin province.
The raid of the consulate by ISIL militants prompted the Turkish government to chair a crisis meeting.
Prime minister Recep Tayyip Erdogan held an emergency meeting with Deputy Prime Minister Besir Atalay and the country's spy chief Hakan Fidan to discuss security measures and how to secure the release of those kidnapped, according to the official.
"We have information that the diplomats were taken to the ISIL headquarters in Mosul," the official said.