He was reportedly held by the al-Qaeda-linked group Hayat Tahrir al-Sham.
HTS, which was once known al-Nusra Front, is the dominant force in the opposition-held north-western Syrian province of Idlib.
Speaking at a news conference on Tuesday, Mr Suga said Japanese officials had been told that the man believed to Mr Yasuda was staying at an immigration facility in the Turkish city of Antakya, which is close to the border with Idlib.
He is being protected by Turkish authorities while his identity is confirmed.
“Given various information, we believe that that the person is highly likely to be Mr Yasuda,” Mr Suga said, adding that the journalist’s wife had already been notified.
Four months ago, a video that appeared to show Mr Yasuda speaking in October 2017 was broadcast by a Japanese TV channel. “I hope all of my family is fine,” he said. “I want to see you.”
The Japan Times reported that the group had demanded a $10m (£7.7m) ransom for Mr Yasuda.
The Japanese government has refused to pay ransoms for hostages.
Qatar has worked to help free other hostages held by opposition armed groups in Syria, including the American journalist Peter Theo Curtis, who was released by al-Nusra Front in 2014.
The Gulf emirate has denied paying ransoms, but has been accused of handing over hundreds of millions of dollars to secure the release of 26 Qataris, including several royal family members, abducted in Iraq by a pro-Iranian militia.