Dagbladet says Solskjaer has 'put Haaland's name on the table'.
It is claimed that Solskjaer wants to sign his compatriot, but a deal may have to wait until the summer.
Solskjaer has also reportedly thought of a number for the Salzburg star amid claims he could cost anything between £50million and £85m.
But whether United can fend off interest from Europe's elite, and others, remains to be seen.
Haaland played under Solskjaer at Molde during his time in his home country.