Balasingham had been the main contact for peace broker Norway as well as other key international players involved in attempts to bring about a peaceful resolution to the island's drawn out Tamil separatist conflict.
Ten years ago, he underwent a kidney transplant.
The London-based official, 68, has led negotiations with the Sri Lankan government since the latest round of face-to-face talks began in September 2002, but he was absent from a meeting in Geneva last month because of failing health.
The Sudar Oli newspaper said Balasingham had been hospitalised since last week.
"He is in an incurable stage with the cancer fast spreading to his liver, lungs and bone-marrow," the newspaper said in a report filed by its editor currently visiting London.