Following Malky Mackay's sacking on Friday the former Manchester United striker and current Molde manager was quickly marked out as Cardiff chairman Mehmet Dalman's number one target to replace the Scot.
Earlier this week it had been suggested Solskjaer, 40, had reservations about taking the job following Cardiff owner Vincent Tan's numerous disputes with Mackay over recent months.
But Dalman remained confident he could convince the Norwegian 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.
Press Association Sport understands the deal for Solskjaer to take over has yet to be completed and negotiations are continuing.
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.
Tan was not due to attend Wednesday's game against Arsenal at the Emirates, but it has been reported he and Solskjaer were flying into London ahead of the fixture for further discussions.
- Sports & Recreation
- Malky Mackay