The Norwegian is in line for his second spell as United manager, with the board ready to appoint a caretaker to the end of the season after Monday's dismissal of Ruben Amorim.
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The Mirror says Solskjaer was planning to take a break from the game after his axing by Besiktas earlier this season.
However, with United in contact, Solskjaer has now decided to end such thoughts and make himself available to his former club.
Solskjaer met with United officials over Tuesday and Wednesday - as did Michael Carrick, who is also in contention for the post.
It's been suggested the pair could yet work together, just as they did during Solskjaer's first spell in charge.