Taner Savut, the club's sporting director, is still trapped, Ozat told Anadolu.
Atsu, who joined Hatayspor last year, previously played for several European teams such as Premier League sides Everton, Chelsea, and Newcastle United, as well as Portuguese club Porto.
Many of his previous clubs posted messages of support and prayers after he went missing.
In a tweet, the Ghana Football Association hailed the "positive news" about the international winger.
"We've received some positive news that Christian Atsu has been successfully rescued from the rubble of the collapsed building and is receiving treatment," the association said.
"Let's continue to pray for Christian," it added.
Over 3,400 people have been killed and more than 20,500 injured in 10 provinces of Türkiye after two strong earthquakes jolted its southern parts on Monday, according to latest official figures.
All sports activities have been suspended until further notice as the country observes a seven-day period of national mourning.
International sports organizations including FIFA, UEFA, EuroLeague Basketball, and sports teams around the world issued messages of condolences and support after the deadly quakes.
