The monarch passed away in the southern Chinese city with his brother, the crown prince, at his bedside after being rushed to hospital, the Matangi Tonga Online said, but there was no immediate confirmation from Tongan authorities
Known to the outside world for eccentricities such as his elaborate uniforms and being driven around in a London taxi, he will be remembered by his subjects for introducing the kingdom's first democratically-elected parliament.
The brief Matangi Tonga report said that "the Crown Prince Tupouto'a Lavaka was there at the hospital just before the king passed away.
"This news is yet to be officially confirmed but our reliable source informed us that the king was rushed to hospital early this afternoon but it is understood that he had passed away a few hours later."
He was unmarried and his brother is heir to the throne.
The report did not say what the cause of death was, but six months ago the king underwent successful surgery to have a kidney removed after a tumour was discovered.
Government and royal palace officials in Tonga were not immediately available to comment on the report but a statement was expected following Monday's cabinet meeting.
Radio Australia said the main religious body in Tonga, the Free Wesleyan Church, had announced it would be holding a prayer service at the official residence of the king's mother in the capital Nuku'alofa.
His other eccentricities included wearing colonial-era pith helmets, sailing model boats in his swimming pool and playing computer games. But to the 115,000 people in Tonga, he was the man who introduced political reforms.
Tupou V was sworn in as king of one of the world's last absolute monarchies in September 2006 following the death of his father king Taufa'ahau Tupou IV.
However his coronation was delayed until 2008 as the tiny kingdom reeled from the impact of riots in the Nuku'alofa.
Eight people were killed and much of the central business district was destroyed in the November 2006 riots when people protested against the slow pace of political reform.
When Tupou V was finally crowned in an ancient Tongan ceremony, more than 200 nobles and chiefs presented dozens of slaughtered pigs and hundreds of baskets of food in tribute.
He was offered a bowl of kava, a mild narcotic drink made from plant roots, to signify his sovereignty over Tonga, a country spread over 170 islands.
Within two years, the Oxford University-educated monarch had made good on his pledge for democracy and the people of Tonga voted in their first popularly elected parliament in 2010 ending 165 years of feudal rule.
The democratic changes replaced the former feudal system where the public could only vote for nine of the 33 representatives in parliament which was dominated by a clique of nobles selected by the king, who also chose the prime minister and cabinet.