Solskjaer replaced Jose Mourinho in December, with Eliteserien side Molde saying they merely “lent” the Norwegian to United until the end of the season.
The 46-year-old has emerged as the favourite to permanently replace Mourinho, having only lost one match during his time at the helm, while United remain unbeaten in the Premier League under Solskjaer.
And as Solskjaer enhances his chances of becoming full-time manager of United, the fan favourite does not know where he stands with Molde ahead of the club’s Champions League last-16 return leg against Paris Saint-Germain.
“I’m not sure how it works. I think the contract is expired and I’m now under contract with Manchester United,” Solskjaer told Norwegian podcast Fotballklubben.
Solskjaer’s only defeat as United boss came against Tuesday’s opponents PSG, who left Old Trafford with a 2-0 first-leg victory last month.
Last week, Solskjaer admitted he would find it “strange” if he was not United manager next term after featuring in promotional videos for 2019-20 season tickets.