"Hashan has played the game for years and he's captained Sri Lanka as well. So it's interesting to see what he has to say and if he has anything more than allegations," Sangakkara was quoted as saying by the Press Trust of India news agency.
Tillakaratne, who played 83 Tests and 200 one-dayers during a 15-year career, claimed last week that Sri Lankan players had been involved in match-fixing since 1992 and added that he was prepared to name some of them.
Sangakkara, captain of the Deccan Chargers franchise in the Indian Premier League, said Tillakaratne should work with the International Cricket Council if there was any basis to his allegations.
"It's dangerous to throw names around," said Sangakkara, who quit as captain after Sri Lanka's defeat to India in the World Cup final last month.
"He should work very closely with the ACSU (Anti-corruption and Security Unit) of the ICC and the home authorities to ensure that something's done about it if there is any foundation to those c