Malky Mackay says he has twice been rebuffed in his attempts to call immediate peace talks with Cardiff owner Vincent Tan.
Mackay was given a 'resign or be sacked' ultimatum by email ahead of Saturday's 3-1 Premier League defeat at Liverpool but stood his ground and was told on Sunday he is safe "for the foreseeable future".
Club chairman Mehmet Dalman is attempting to broker urgent talks between owner and manager but, according to Mackay, Tan has so far declined two offers to meet.
He said: "I've been asked if I would meet the owner and Mehmet which is absolutely something that would be for the good of the club going forward. I think that should be sooner rather than later.
"I certainly wanted that meeting to be today, but unfortunately that was declined. If not today, then tomorrow - but unfortunately that's also been declined.
"After that, we're into Christmas Day and then there's a game day, so unfortunately that's not going to be until the end of the week."
Mackay, who was "deeply hurt" by Tan's now-infamous email and expected the sack at the weekend, praised Dalman's role in offering to mediate.
But he said: "Ultimately Mehmet's not the one making the decisions that have led to this point, and that's something that still has to be addressed."
In the meantime, Mackay, who continues to enjoy the backing of his players and the club's supporters, has made it clear it is business as usual ahead of Southampton's Boxing Day visit.
He said: "My situation doesn't change. I want to be the manager here, I'm proud to be the manager here, I think I should be.
"Our players, our supporters and our staff are all backing the one way forward, so I keep doing what I'm doing and I don't change that. If someone wants to do something different, then that's up to them."
Speaking on Sunday, Dalman was unable to guarantee Mackay's long-term future but was hopeful of finding a solution.
The City chairman explained: "We managed to create space for everyone to work together back in October and we have to see if we can do that again in order to move forward.
"At least we have a platform for dialogue, which gives us an opportunity to try to work our way through this.
"Let's see if we can fix it. We can't keep having the club under a cloud, so this is it. We managed to get two or three months leeway last time and we need to create something similar again. I'm not putting a timescale upon this, but we have to try."