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 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.
In an interview broadcast on Tuesday on BBC Radio Wales, Mackay said: "I will not resign from my post. I was surprised obviously, but at the same time my job doesn't change.
"It's a job only three-quarters done as far as I'm concerned - making Cardiff a sustainable Premier League team.
"I have a great group of players who are competing at this level and enjoying this level. The fans are enjoying being at this level and my duty is to make sure we continue to do that.
"It would be wrong of me to walk away from a job because the owner doesn't want to give me more money in January."
On Thursday, Mackay received support from Liverpool manager Brendan Rodgers who Cardiff face on Saturday.
"I find it astonishing, what he's had to go through," said Rodgers, who worked with Mackay when he managed Championship side Watford in the 2008-2009 season.
"He's going to go on and become a big manager at a top club and I find it astonishing there's talk about him leaving there, absolutely astonishing.
"My only conclusion when I look from the outside is you've got a business guy operating the club who obviously knows nothing about football.
"He's (Tan) obviously been a very successful business man in his life, but football is like no other business."