Tan, who claims he spent a total of £50million on deals over the summer, warned Mackay on Monday night he will receive "not a single penny" for transfer window deals.
And with Tan also said to be "extremely upset" over Mackay speaking out about deals before putting his plans to the board, the situation exposes a major difference of opinion at the top of the club.
Mackay claimed at the weekend, after a 1-0 win against West Brom, that he hoped to bring in three new players to fortify his team for the second half of their maiden Barclays Premier League season.
Chief executive Simon Lim released a statement that outlined Tan's disappointment with Mackay.
"Tan Sri Vincent Tan was extremely upset to read quotes from the manager concerning the possibility of new recruits, before he had been informed whether funds would be made available," Lim said.
"He believes that doing so unfairly raises supporter expectations, placing unnecessary pressure on the club.
"His view is that due to the funds already committed, including the originally authorised summer transfer budget of £35million that rose to £50million in total, including add-ons, the manager has been fully supported.
"The overspending of £15million has upset Tan Sri greatly, resulting in the removal on Iain Moody as head of recruitment. As such, he has stated that not a single penny will be made available in January.
"Having been the highest-spending promoted club and the seventh-highest spender in the Premier League last summer, the owner believes that the manager has been given the best possible chance of retaining our Premier League status."
Moody was replaced by Kazakh 23-year-old Alisher Apsalyamov in October.
If Mackay survives to lead the club in January he may have little option but to sell players to fund deals, if Tan refuses to be swayed on his insistence there will be no budget for the Scot to utilise.
Cardiff brought Steven Caulker, Gary Medel, Kevin Theophile-Catherine and Andreas Cornelius to the club during the summer.
Speaking at the weekend, Mackay said: "It would be great if we can bring in three quality additions to the squad.
"I would look to strengthen all three departments in terms of a defender, a midfielder and an attacking player.
"I will talk to my chairman (about January) who will then discuss it with his board of directors and our owner and I will take my lead from them."
He added: "It's about bringing in another layer of quality to add to what we've got. I need to bring in guys who are going to add to that."
Mackay joined Cardiff in June 2011, and after missing out on promotion in his first season at the club, when his team suffered a play-off semi-final defeat to West Ham, he led the Welsh side to the 2012/13 Championship title.
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