There has been no official announcement that the Norwegian is taking over from Jose Mourinho, who was sacked earlier on Tuesday.
But a page on the club's website referred to their ex-striker as "our interim manager". It was later deleted.
Solskjaer, 45, scored 126 goals for United in 11 seasons with the club under Sir Alex Ferguson.
He is in charge at Norwegian side Molde but their 2018 season has finished for the winter and does not re-start until March.