Sky Sports TV pictures showed the former Manchester United striker and Tan arriving together at the Emirates Stadium on Wednesday ahead of Cardiff's Premier League clash with Arsenal.
Solskjaer was installed as favourite to take over in South Wales when Malky Mackay was sacked last Friday following a series of disputes with the club's controversial owner.
When asked about the appointment, Solskjaer told Sky Sports: "I have nothing to say at this point. I just want to enjoy the game first."
Betting has been suspended after Norwegian television reports suggested Solskjaer had agreed to take the job. He was 1/4 with Sky Bet before midday on Wednesday.
Following Mackay's sacking on Friday the current Molde manager was quickly marked out as Cardiff chaiman Mehmet Dalman's No.1 target to replace the Scot.
Solskjaer has enjoyed a successful spell in charge of Molde, guiding them to two Norwegian titles and a Norwegian Cup.
He turned down the chance to become Aston Villa manager prior to the appointment of Paul Lambert at Villa Park, while he had also been linked with the current vacancy at West Brom.
Dalman stated last week he had one candidate in mind and refused to deny he had held discussions with Solskjaer, saying: "I might have and I might not have".
Caretaker boss David Kerslake, Mackay's assistant, has taken charge of the team on a temporary basis and will oversee the team's tough trip to Arsenal on New Year's Day.
He held brief talks with owner Tan ahead of Saturday's 2-2 draw with Sunderland, but was not told how long he will remain at the helm.
"I don't know anything. It's as we were the last game. I've been told to take temporary charge of the team and that's the only thing that I know," said Kerslake.
Asked whether he knew if Cardiff were close to an appointment, Kerslake replied: "No, absolutely in the dark on that situation.
"I spoke to the owner, chief exec and the chairman before the game against Sunderland and it was just really thanking me for taking the team and wished me well."
Solskjear's agent was trying last minute to negotiate out a couple of clause's Tan had inserted in the contract. 1. Players must all be born on a hobgoblin tuesday. 2. Ole and his staff must adhere to the policy of wearing trouser's at nipple height at all times. 3. they will publicly support the forth coming decision to change the club name to simply sausages super-super red dragons of Cardiff City F.C.- kernowpete