The discussions follow the sacking of Ruben Amorim after 14 months in charge, with under-18s coach Darren Fletcher currently acting as interim.
Solskjaer, who previously managed United from 2018 to 2021, is considered a strong candidate for the interim role due to his long history with the club.
United are seeking an interim appointment to allow time for a permanent manager to be appointed in the summer.
Crystal Palace boss Oliver Glasner is a top candidate for the permanent position, with Kieran McKenna, Enzo Maresca, and Julian Nagelsmann also being considered.