Tan sent Mackay a detailed letter by email on Monday, which concluded with the Malaysian ordering the Scot to quit the club or face dismissal. It is thought to be highly unlikely that Mackay will resign.
Press Association Sport understands discussions have taken place between club directors throughout Friday, with Tan set to arrive in the UK this evening ahead of his attendance at Saturday's Barclays Premier League fixture at Liverpool.
It is understood Mackay took training, which was closed to the media, this morning and footage has emerged of him at Cardiff Airport as the squad prepared to depart for Merseyside.
Meanwhile, a small group of supporters have gathered at Cardiff City Stadium to protest against Tan's running of the club.
Mackay had been due to face the media this morning ahead of the game at Anfield, but instead it was his assistant David Kerslake who spoke at a press conference which lasted barely five minutes.
And Kerslake refused to discuss Mackay's situation.
He said: ''I am here to talk about the Liverpool match, I came in this morning and was asked to do the press conference.
''Malky is in the training pavilion as we speak, we are just here to talk about the game.''
When asked if Mackay was still in charge, Kerslake added: ''No one has said any different to me, everything has been as normal. Players have got on with their jobs.
''Without being boring it has been a normal week.''
When Kerslake came in for more aggressive questioning on Mackay's position a club spokesman stepped in to say: ''Malky Mackay is unavailable to speak to the media, the assistant manager is here.''
He later added: "Malky Mackay is still in charge, I have spoken to Malky this morning."
When faced with further queries on Mackay, Kerslake consistently replied: ''I will answer any questions you have about the game of football tomorrow.''
Tan's email to Mackay outlined his grievances with the former Watford boss at great length.
Tan was highly critical of Mackay's signings, style of play, results and performance as a manager.
The letter concluded with the ultimatum that the Scot quit or be given the boot by the controversial Malaysian businessman.
Mackay, who led Cardiff to the 2012 League Cup final before securing the Championship title last term, has previously stated he would not resign from his position, and it is believed it could cost Tan somewhere in the region of £3million to sack the 41-year-old, whose contract runs until 2016.
Mackay's position as Bluebirds boss has been under scrutiny since Tan removed his head of recruitment Iain Moody in October amid suggestions of a summer transfer window overspend, something the Scot and Moody denied outright.
The problems at the club deepened on Monday, the same day as Tan's email was sent, when chief executive Simon Lim released a statement claiming Tan was ''extremely upset'' at Mackay's comments that he hoped to bring in three players in January, and that there would not be ''a single penny'' available to spend next month.
The latest row with Tan has also seen odds on the Scot becoming the next West Brom manager slashed.
Former Manchester United striker and current Molde boss Ole Gunnar Solskjaer, as well as ex-England manager Sven-Goran Eriksson have already been tipped as possible replacements for Mackay.
Turkish manager Yilmaz Vural has also emerged as a contender; just a matter of weeks ago Cardiff chairman Mehmet Dalman had denied knowing who the 60-year-old, who has managed over 20 clubs in his homeland, even was.
Dave Jones, Bluebirds boss between 2005 and 2011, had also been mentioned, but a return to the Welsh capital for the former Sheffield Wednesday manager is thought to be unlikely.