After Monday's dismissal of manager Ruben Amorim, United are in advanced negotiations with Solskjaer about taking the job to the end of the season.
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It will be the second time Solskjaer has taken charge of United, having spent three seasons as manager after an initial caretaker's role to succeed Jose Mourinho.
Nettavisen is reporting Solskjaer and United are now discussing a contract based on around £50-60,000-a-week - and heavily laden with bonuses.
United are two points outside the top four and Solskjaer could receive between £3m-£4m if he secures them a spot in the Champions League.