The former Manchester United striker and current Molde manager attended Wednesday's defeat to Arsenal at the Emirates Stadium in the company of owner Vincent Tan and chairman Mehmet Dalman, and his appointment would appear a formality.
Press Association Sport understands a deal has yet to be completed, but the Welsh club fully expect to present the Norwegian as Malky Mackay's successor on Thursday.
Solskjaer has been Dalman's number one choice to succeed Mackay in the wake of the Scot's sacking last Friday.
However, earlier this week it had been suggested Solskjaer had reservations about taking the Cardiff job following controversial owner Tan's numerous disputes with Mackay over recent months.
Nevertheless, Dalman remained confident he could convince the 40-year-old to take over at Cardiff City Stadium with the promise of money to spend in the January transfer window and reassurances over the working structure at the club.
Tan had not been scheduled to attend Wednesday's game at the Emirates, but flew into London especially to try to push through the deal.
And Cardiff midfielder Aron Gunnarsson hopes Solskjaer can bring a buzz to the club.
He said: "We are working ever so hard to prove our point on the pitch and get respected in the Premier League as we want to be in this league.
"I have heard he has done well with Molde in Norway. Hopefully he will bring something new, different and exciting into this club."