Cardiff caretaker manager David Kerslake told reporters he had heard nothing about any appointment and it was "business as usual" ahead of Saturday's FA Cup tie at Newcastle United but British media reported that an announcement was expected soon.
Arsenal manager Arsene Wenger said he had seen Solskjaer, who is manager of Norwegian side Molde, before the game and Cardiff "played like they knew he was in the stand".
However, former Tottenham Hotspur defender Kerslake played down any influence Solskjaer may have had on the Welsh team's battling performance, saying: "There was no talk of it on the team bus, in the hotel or in the dressing room."
Cardiff held league leaders Arsenal at bay until the 88th minute when substitute Nicklas Bendtner scored before Theo Walcot added a second goal for the hosts in stoppage time.
The result leaves promoted Cardiff one place and one point above the relegation zone with 18 points from 20 matches after taking one point from their last four league games.
Norwegian media earlier reported that Solskjaer had flown from Kvernberget airport in Kristiansund, close to his home, in a Malaysian-registered private jet for the Arsenal game.
Citing sources close to the board of Molde, where Solskjaer has been manager for the past three seasons, Norway's TV2 reported that negotiations were at an advanced stage and that he was due to take over before the third round game at Newcastle.
NOT RISKY
Experienced Frenchman Wenger said it was not a risky appointment for Cardiff or Solskjaer.
"Basically what you want when you're young is 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."
Wenger added that he thought Cardiff were the fittest team in the league and that apart from strengthening their striking options they had the "basic ingredients to survive".
Solskjaer, the hot favourite to succeed Malky Mackay, was chatting and laughing alongside Cardiff's controversial Malaysian chairman Tan during Wednesday's game.
Mackay was sacked on December 27, seven months after winning promotion to the top flight.
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.
(Additional reporting by Philip O'Connor in Stockholm and Mitch Phillips in London; editing by Ed Osmond and Ken Ferris)
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