Tan told Mackay early last week to resign or be sacked but chairman Mehmet Dalman said on Sunday that the manager would remain in his post for the foreseeable future.
"There are certain areas that have to be addressed that were in the email," Mackay told a news conference ahead of sixth-from-bottom Cardiff's Boxing Day fixture at home to Southampton.
"I wanted a meeting (with Tan) today but unfortunately that was declined. If not today, then tomorrow, but unfortunately that was also declined.
"I don't know if we can talk. Mehmet has been trying to do this for three months, as have I," added Mackay.
"I will find out when I go to the meeting. At that point I will take stock of where I am."
Mackay, who guided Welsh club Cardiff back into the top flight for the first time in 51 years last season, again reiterated that he would not quit as manager.
"I did feel I was going to lose my job at the weekend," he said. "The email deeply upset me.
"I declined to resign and expected to be sacked. Mehmet is a good man and a sensible man but he's not the man who makes the decisions.
"Ultimately he will not make the decision. I'm proud to be the manager here and I think I should be the manager," added Mackay.
"I will keep doing what I'm doing and if someone wants to do something different that's up to them."