The 33-year-old told a prominent English paper that he had been contacted by telephone and asked to throw a Davis Cup match early in his career.
"I haven't been approached in the context of an ATP (tournament). I was approached maybe 10, 12 years ago, in the context of Davis Cup in India," the winner of 10 grand slam titles in men's doubles and mixed doubles said in an interview.
"I immediately changed my phone numbers and I never got that call again. It definitely freaked me out."
Bhupathi is the latest in a growing list of players on both the men's and women's tours, including former top-10 player Arnaud Clement of France, to admit that they had rejected offers to lose a match.
The ATP, which governs the men's game, is investigating a match between world number four Nikolay Davydenko of Russia and Argentina's Martin Vassallo Arguello, played in Poland last August.
Davydenko retired at 2-1 down in the third set of their match, citing a foot injury, but British exchange betting company Betfair reported irregular betting patterns on the match and voided all bets.
Three Italian players, Potito Starace, Alessio Di Mauro and Daniele Bracciali recently received suspensions and fines for gambling on tennis matches.
Bhupathi said the scandals were tarnishing the reputation of tennis.
"It's sad, terrible for the sport," he said.
"I wish the ATP could find as many ways as they can to control it. (There is) so much money at stake and so many different avenues the players can use.
"So I am glad that they are punishing players now, so guys will at least get a little more weary. Tennis is a great sport, we must find ways to protect it."