Mackay had been widely expected to be sacked by Tan after the owner sent him an email last week criticising his managerial abilities and concluding with an ultimatum that the Scot resign, or face being dismissed.
Mackay has stated on several occasions he will not resign and his departure looked imminent after the weekend loss at Liverpool.
But chairman Mehmet Dalman, a close ally of Mackay’s, said on Sunday the 42-year-old would be in charge for the “foreseeable future”.
However, included in Dalman’s comments was the caveat that there would need to be some form of reconciliation between owner and manager.
That would be a big surprise given the ill-feeling between the two men which intensified following Tan’s removal of Iain Moody as his head of recruitment in October.
Press Association Sport understands Alisher Apsalyamov, the Kazakh who took over Moody’s role in an acting capacity, has left the club having initially stood aside temporarily due to visa issues.
Tan was also furious at Mackay’s expression of his hopes of adding to his squad in January, with his incendiary email of last week following in short order.
But Mackay has twice had requests to meet with Tan and Dalman to try and iron out their differences turned down.
“I have read Mehmet’s statement and I’ve been asked if I will meet Mehmet (and Tan) which is absolutely something that would be for the good of us and the club going forward,” said Mackay.
“I think that should be sooner rather than later
“I wanted that meeting to be today but that was declined. If not today, then tomorrow but that was also declined.
“After that we are in Christmas Day and then it’s game day so unfortunately it is not gong to be until the end of the week.
“In the meantime I will do my job. ”
Mackay revealed he had been “deeply upset” by Tan’s attack on him, and had expected to be sacked over the weekend.
“I did feel I was going to lose my job on the weekend,” he said. “The email deeply upset me.”
But the Scot reiterated he will not be quitting his role.
“If it’s anything to do with me I will still be the manager. I won’t be resigning from the football club.
Saints, meanwhile, have now gone six matches without a win following their defeat by Spurs on Sunday but midfielder James Ward-Prowse is confident they will soon come good.
“We’re disappointed to lose again,” the 19-year-old midfielder said.
“I think we were just beaten by a good Tottenham side, who were galvanised under the new manager.
“It’s a test of character for us, and I know we’re mentally strong enough to get through that.”