Norwegian media earlier reported that Solskjaer had flown from Kvernberget airport in Kristiansund, close to his home, in a Malaysian-registered private jet.
Citing sources close to the board of Norwegian club Molde, where Solskjaer has been manager for the past three seasons, TV2 reported that negotiations were at an advanced stage and that he was due to take over before Saturday's FA Cup tie against Newcastle United.
Solskjaer, the hot favourite to succeed Malky Mackay, sat alongside controversial owner Tan at the Emirates Stadium during Wednesday's game and was seen to be chatting and laughing.
Mackay was sacked on December 27, seven months after winning promotion to the Premier League.
Solskjaer has won two league titles and the Norwegian cup since taking over at Molde, and was previously linked with vacancies at Aston Villa and West Bromwich Albion.
Arsenal manager Arsene Wenger said after his side's 2-0 win that Solskjaer has all the ingredients to help keep Cardiff in the Premier League.
Wenger, who is now the longest serving manager in the English top flight, sees no reason why Solskjaer cannot make a success of what would be a first major managerial role.
"I have seen him before the game, and they played like they knew he was in the stand," said Wenger.
"Cardiff has the basic ingredients to survive in the Premier League.
"You would say if you look at their record they need to add a bit more goals offensively to stay in the league.
"If he (Solskjaer) can find that in the final third something clinical like he was, then they will stay in the league because they have the basic quality to do it."
Wenger continued: "It is a chance (for Solskjaer).
"Basically what you want when you are young is a chance and after you have to make the maximum of that chance.
"He has already experience as a manager in Norway, so he has learned his job.
"He was an intelligent player, so he is an intelligent boy as well, and that will help him to be successful."