BBC cricket commentator was reportedly met with silence when he told a crowd that he had a better chance of getting a knighthood if he "blacked up".
During a question-and-answer session at Birmingham's Egbaston ground he told Sky Sports presenter Gary Newbon that knighthoods had been given to great players from the West Indies like "confetti" but added "mine's been turned down twice. I'd better black me face."
The Mirror reported that the event, which took place during a break in play on Saturday (19 August), included black guests and that the commentator's words were met with silence.
A source told the paper: "It was a crass comment. It was intended to get a laugh but it went down like a lead balloon. People were offended."
"Is Boycott suggesting these great West Indians got knighthoods merely because of the colour of their skin? Birmingham is celebrated for its ethnic diversity and racial tolerance.
"We can do without dinosaurs like him spouting rubbish."
There have been 11 West Indian players to get knighthoods, including greats like Sir Viv Richards and Sir Clive Lloyd.
An activist from Birmingham, Desmond Jaddoo, said that Boycott's comments were "like something from the dark ages" and "ill-advised and ill-conceived".
"He should take a long, hard look at why he doesn't have a knighthood rather than offending those who do have one," he told the Mirror.
Boycott, who did not respond to requests for comment, played 108 tests for England, scoring 151 centuries. He holds an OBE but claims he has not got a knighthood due to his conviction for beating his ex Margaret Moore in 1996. He has been a BBC commentator since 2004.