The former Manchester United striker and current Molde manager is the bookmakers' favourite to take charge of the Bluebirds after Mackay's dismissal on Friday.
Dalman made an unexpected appearance in the post-match press conference room after the 2-2 draw with Sunderland, and said discussions have already taken place with his preferred candidate, but would not confirm whether it was Solskjaer.
"I have a preferred candidate. I only have one candidate in mind," he said.
"I have not made an offer to anybody as such, but that does not mean I have not had discussions."
When asked if he had spoken to Solskjaer, he said: "I spoke to him many a time in the old days (when the Norwegian was at Manchester United).
"I might have spoken to him recently, and I might not have."
He added: "You know what these things are like, they take time. We will do our work as diligently and as quickly as we can but I am reasonably optimistic that we will get things moving."
One man Dalman ruled out of contention is Turkish journeyman Yilmaz Vural.
Vural's agent has consistently touted him for the Cardiff job, but Dalman said: "I am not getting a Turkish manager, I can categorically state. There is a manager who keeps putting himself forward. It is not going to happen."
Dalman confirmed Mackay's lieutenants David Kerslake and Joe McBride will remain in temporary charge of the team against Arsenal on New Year's Day.
Kerslake made it clear he has no aspirations to take the full-time job.
He said: "I have been in the position for six hours and had three phone calls from the director, one from the chief executive, one from the chairman and one from the owner. That's probably put me off for life!
"They were all well wishes as well, by the way, but I have been a coach for 10 years. I love what I do. I love being on the grass with the players."
Cardiff should have taken all three points against the Black Cats after dominating the first hour and leading 2-0 through Jordon Mutch and Fraizer Campbell goals, only for the visitors to hit back through Steven Fletcher and Jack Colback late on.
Owner Vincent Tan was pictured booing after the final whistle, however it was unclear if Cardiff's players were his target.
Kerslake praised how the team responded, having learned of Mackay's sacking on television.
Kerslake said: "The players are devastated in the dressing room. We got ourselves in a fabulous position and we should have seen the game out.
"It is disappointing for us because we were 2-0 up. With eight minutes to go, we conceded a poor goal so there is work to be done."
Kerslake added: "The players found out (about Mackay) via the TV. I guess they are only human and they have probably been on the phone talking about it.
"The way we came out the traps today they certainly put it behind them.
"The manager has asked for that start for the last two-and-a-half years and to come out all guns blazing. For 35-40 minutes, we blew Sunderland away."
The sacking of Mackay has been widely condemned and ensured the spotlight was firmly on the home side, but there were no signs of any genuine venom being directed towards owner Tan, although there were several pro-Mackay chants and banners in evidence throughout the game.
- Sports & Recreation
- Manchester United