Norway's TV2 said that a Malaysian-registered private jet had landed at Kvernberget airport in Kristiansund, close to where the 40-year-old Solskjaer lives.
Citing sources close to the board of Norwegian club Molde, where Solskjaer has been manager for the past three seasons, TV2 reported that negotiations are at an advanced stage and that he is due to take over before Saturday's FA Cup tie against Newcastle United.
TV2 said that a plane registered to Berjaya Air - owned by Cardiff City owner Vincent Tan - and destined for London's Luton airport took off at 1050 local time.
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.
Previous Cardiff City manager Malky Mackay was sacked on December 27, seven months after winning promotion to the Premier League.
Cardiff, who play Premier League leaders Arsenal on Wednesday, are 16th in the table at the halfway point of the season.
Image: Ole Gunnar Solskjaer
Photograph: Sara Strandlund/EuroFootball/Getty Images
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