According to NTV television, an F-16 fighter plane was scrambled as soon as the pilot signaled there was a hijacking attempt and escorted the plane to Istanbul's Sabiha Gokcen airport.
Turkey's state-run TRT television said authorities convinced the man to give himself up and he was taken into police custody, but there was no confirmation from the Transport Ministry.
There were 110 passengers on board flight from Kharkiv, Ukraine, but it was not immediately clear if they had evacuated. Authorities were searching the plane.
Habib Soluk, the Turkish Transport Ministry undersecretary, told NTV that the man rose from his seat, shouted that there was bomb on board and tried to enter the locked cockpit. The pilot signaled that there was a hijack attempt and the airport was placed on high alert.
"The man was made to believe the plane was heading to Sochi," Soluk said. "We are hoping that the passengers are evacuated without even a nose-bleed."
The Interfax news agency cited the Ukrainian Security Service, the country's main security agency, as saying the passenger who tried to hijack the plane was in a state of severe alcohol intoxication.
Pegasus Airlines confirmed in a brief statement there was a "bomb threat" aboard their flight from Kharkiv.
The plane's captain, Ilyas Karagulle, signaled that the crew was well, according to state-run TRT television.
With about 100,000 police, security agents and army troops flooding Sochi, Russia has pledged to ensure "the safest Olympics in history." But terror fears fueled by recent suicide bombings have left athletes, spectators and officials worldwide jittery about potential threats.
Security experts warn that Islamic militants in the Caucasus, who have threatened to derail the Winter Games that run from Feb. 7-23, could achieve their goal by choosing soft targets away from the Olympic sites or even outside Sochi.