"There is news that excited everyone. Rescuers pulled a child alive," Sawyer said on Twitter.
As the NTV channel reported, the four-year-old girl has been pulled from the rubble and is taken to the hospital in satisfactory condition.
The Disaster and Emergency Management Authority reported that 102 people died in the earthquake, and 1,026 were injured, of whom 143 are still being treated in hospitals.
A 6.6-magnitude quake toppled more than a dozen buildings in Izmir last Friday. The shock reached the Greek island of Samos in the Aegean Sea, killing two teenagers and injuring 20 people.