"He told me his syndicate were involved in making money as the game fluctuates.
"I said, 'You've got the wrong person'.
Players and umpires who get involved in match-fixing have got to realise there's no such thing as easy money.
"Once you get into that, your career is ruined.
You'd lose your self-respect, the players and commentators would know.
"I couldn't live my life looking over my shoulder, and I'd always be remembered as a cheat, so I had to say no, and reported it.
"
Holder, who stood in 11 Tests, said the approach related to a match between Sri Lanka and Pakistan in Sharjah.
"They said if I can somehow lull the Sri Lanka batsmen into putting on a partnership of 85 they would give me £10,000 in cash," the 68-year-old Holder told BBC Radio's Test Match Special.
"I said, 'You've got the wrong person'."
Barbados-born Holder, a former bowler for English county Hampshire, became a first-class umpire in 1983 and stood in 11 Tests and 19 ODIs from 1988 to 2001.