Paddy Power briefly advertised odds of 66/1 on ex-Aston Villa and England defender Ugo Ehiogu taking charge of rivals Birmingham City, following the sacking of manager Harry Redknapp on Saturday.
Ehiogu, who also played for Middlesbrough and Rangers, died at the age of 44 after suffering a cardiac arrest on April 20 at Tottenham's training ground, where he worked as a coach with their under-23 side.
The likes of former England manager Sam Allardyce and ex-Crystal Palace boss Frank de Boer were included in the market at odds of 33/1.
Other options were long-serving Villa striker Gabriel Agbonlahor (275/1) and veteran Birmingham rocker Ozzy Osbourne (2,500/1).
Ehiogu's inclusion provoked anger on social media.
Tom Wainwright said it was "sick" that punters could bet on the former centre-back, while David Kelly said it was "pretty poor taste".
Matt Zarb-Cousin, or the Campaign for Fairer Gambling and a former spokesman for Jeremy Corbyn, said he hoped it was "a mistake not a joke".
Replying to Twitter users individually, Paddy Power said it was "a genuine error, which was removed as soon as we realised. Apologies".
The company later issued a statement to the Press Association, adding: "This was a genuine error, a trader re-used an old market as a template for this one, and didn't notice that Mr Ehiogu was included.
"Obviously, that was a mistake, one which was rectified as soon as it was spotted, within minutes."
A spokesman said customers were able to put money on Ehiogu for "less than five minutes" before the error was discovered, adding that nobody actually placed that particular bet.
He added: "We would like to apologise to Mr Ehiogu's family if they did see the tweet.
"It was obviously a mistake and no offence was meant."