Reports suggest the controversial Malaysian businessman attended a team meeting before the weekend's 1-0 defeat to Tottenham and told the squad they would share a £7.4m pot if they retain their Premier League status.
The bonus would have contravened the league's regulations, which state that any bonus be officially lodged before the start of the season and not offered on an ad hoc basis, but Cardiff were quick to play down the situation.
Cardiff chairman Mehmet Dalman told Sky Sports News: "This has all been taken out of context and is a misunderstanding.
"Yes, Vincent did make the offer on Saturday but he has no executive powers. He's just the owner. He's not running the club and it wasn't up to him to make this offer.
"I've told him there are strict rules about bonuses and we'd talk further about implementing with the payment structure for next season. Please bear in mind, Vincent Tan meant well on this occasion."
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."