The Norwegian man can be seen in a surveillance video taken during the attack, the channel reports, firing off shots at Kenyan police as they try to storm the terrorists.
Norway's intelligence services PST last week disclosed that they were investigating the role a Norwegian citizen played in the attack, after receiving information on the 23-year-old.
According to VG newspaper, the man came to Norway in 1999 and has worked as a telemarketer and warehouse employee.
PST on Monday spent several hours interviewing a relative of the man, who, VG reports, knew nothing about the suspect's involvement in radical terrorist groups.
According to the relative, the man was in Somalia the last time they spoke.
According to TV2's sources, the man had left Norway and join Al-Shabaab, the radical Somali group.