Regulations state that any bonuses must be officially lodged before the start of the season and not offered on an ad hoc basis.
Cardiff are unlikely to face disciplinary action from the Premier League board, however, after a club spokesman said Tan had been unaware of the rules and has since withdrawn the offer.
Punishment for the offence could theoretically stretch to a fine or a points deduction.
League rules state: "Full details of a player's remuneration including all benefits to which he is entitled whether in cash or in kind shall be set out in his contract.
"The terms of a contract between a club and a player shall be strictly adhered to."
Tan reportedly told his players before the 1-0 defeat by Tottenham at the weekend they would share in a £3.7million bonus payment if Cardiff retained their place in the Premier League.
Such bonuses are commonplace as top-flight status means more income for clubs, but they must be made clear in players' contracts or a bonus schedule before the start of the campaign.
A spokesman for Malaysian businessman Tan told The Sun: "Vincent didn't realise it was against the regulations.
"He has since rescinded the offer, which he made only with Cardiff's best interests at heart."
Tan reportedly addressed his players at their hotel, the Hilton in Park Lane, before the match, where he advised them to "shoot more" if they wanted to avoid the drop.
He also apparently took the opportunity to reveal details of the bonus for avoiding relegation.
- Sports & Recreation