NIS wouldn't confirm the two lawmakers' details about Jang, which came in a closed-door intelligence briefing. One of the lawmakers, Jung Chung-rae, said the NIS didn't tell him how it obtained the information.
The other lawmaker, Cho Wonjin, said the spy agency reported that North Korean authorities were investigating corruption allegations involving Jang's aides and that they had been executed.
Jang was last seen in North Korean media on Nov. 6.
South Korean intelligence officials have erred previously in predicting changes in the secretive North, and senior North Korean officials occasionally disappear from state media reports and then reappear.
Jang in recent years has gained top party and military posts, including vice chairmanship of the powerful National Defense Commission and membership in the ruling Workers' Party's political bureau. Jang has also been a frequent companion of Kim Jong Un on his tours around the country, as he was for Kim Jong Il.
He also served as a leading economic policy official in charge of the push to draw foreign investment, traveling in 2012 to China to discuss the establishment of special economic zones. Over the past, he assumed responsibility for North Korea's burgeoning sports industry, a pet project of Kim Jong Un's.