Bateman has refused to name the alleged briber
The 36-year-old claims he was approached before Wales' Five Nations away match against Ireland in 1990.
Bateman's statement follows a similar claim from fellow centre Mark Ring, who said he had been offered £30,000 to lose the same match.
Bateman makes the revelation in his new autobiography, Allan Bateman: There and Back again, which is released next month.
After taking legal advice, Bateman decided not to name the alleged briber.
"At first I mentioned the person who had offered it. But the solicitors advised me he could sue and thought it would be wise to take the name out," Bateman told a national newspaper.
Former Wales full-back Paul Thorburn, who played in the match in question, expressed his surprise at Bateman's claims.
Thorburn insisted he had never been approached to throw a game - despite being Wales' goalkicker for a number of years.
He said: "I could understand if he (Bateman) had said he was offered £200,000 to persuade the rest of his teammates to throw the game.
"But I can't see how one or two players can effect the result of a team game such as rugby."
Joke
Journalist Paul Rees, who co-wrote the book, revealed to BBC Wales Sport that the culprit was not a former player.
He also said that Bateman did not take the bribe seriously.
"If you are a goalkicker you can miss kicks, but I don't think Allan knew how he could throw a game," said Rees.
"He felt at the time the offer might have been made almost in jest. But he couldn't tell one way or another.
"It never entered his head to accept it, although £5,000 was a hell of a lot of money for an amateur rugby player back then."
Wales lost the match in Dublin 14-8 - a result which completed Wales' first ever white-wash in the competition.