Dalman says Cardiff are looking for a swift resolution to the situation and a meeting between Mackay and owner Vincent Tan will take place within a week or possibly on New Year's Day.
Mackay reiterated on Monday that he would not quit the club after receiving an ultimatum from Tan last week to resign or face the sack following a disagreement over transfers.
Dalman said: "Every effort that can be made is being made to allow the club to move forward. We will do everything humanly possible to maintain the status quo but if not we will move fast to repair the situation.
"If that means bringing in a new manager, we will, but for the time being, we believe that's premature and we will work together to fix the predicament we're in."
Mackay, who had expected to be sacked at the weekend before being given a reprieve of sorts, said on Monday that he had twice been rebuffed in his attempts to call immediate peace talks with Tan.
Cardiff host Southampton on Boxing Day followed by another home game against Sunderland on Saturday.
Meanwhile, Mackay has urged the fans to get behind the team when they host Southampton after being left 'humbled' by their support.
The Scot is happy for the fans to give vent to their feelings on Thursday but he also wants them to back his team as they have done throughout the campaign.
"Our fans are the lifeblood of the club," said Mackay.
"When I'm gone and the owner is gone the fans will still be supporting the team. What they want to sing and what they want to say is down to themselves.
"They are intelligent people who have got their own opinions about the football club but I know they will get behind the football team like they have always done from the first day I have arrived there.
"I will always be thankful for that. If they do that then there can be enjoyment of watching their team in the Premier League."