Press Association Sport understands Tan has told Mackay to resign or face being sacked.
The 41-year-old Scot had been due to face the media ahead of Saturday's Barclays Premier League fixture against Liverpool, but instead it was his assistant David Kerslake who spoke.
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 sterner 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."
Faced with further queries on Mackay, Kerslake said: "I will answer any questions you have about the game of football tomorrow."
Source: PA
Source: PA