Azhari Husin and Nordin Mohd Top are wanted in connection with last year's Oct. 12 Bali bombing and the Marriott Hotel blast in Jakarta on Aug. 5, Indonesia's Star reported in its Monday edition.
Azahari, a former lecturer with Universiti Teknologi Malaysia and an explosives expert, allegedly made the bombs for both attacks, the Star said.
The two men are believed to be carrying bombs strapped to their bodies.
Thousands of police have been deployed to Bandung and the West Java towns of Subang, Sukabumi, Garut and Tasikmalaya, the Star said. Police are searching towns' borders, shopping malls and hotels.
The two had a narrow escape last Wednesday from a police raid on their rented house in Bandung, the Star said.
Notable deaths of 2014 [PHOTOS]