United sacked Jose Mourinho on Tuesday after having suffered their worst start to a season for 28 years.
A source close to the club has told Reuters that former United striker Solskjaer and their ex-assistant coach Mike Phelan were set to return to Old Trafford as caretaker managers until the end of the season.
Solskjaer currently manages Norwegian side Molde but their 2018 season has finished for the winter and does not restart until March.
The 45-year-old played for United between 1996 and 2007 and scored 126 goals, including the injury-time winner in the 1999 Champions League final against Bayern Munich.
The BBC reported that United had posted a video featuring Solskjaer scoring the winner against Bayern with the caption reading: "Solskjaer becomes our interim manager, 20 seasons after clinching the Treble with THAT goal at Camp Nou..."
The page was later deleted, the BBC said.
United, who are sixth in the league and trail leaders Liverpool by 19 points, face Cardiff City in the league on Saturday.
Solskjaer was manager there for nine months in 2014, during which time the club were relegated from the top flight and had a poor start to the new season in the Championship. (Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford )
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