The Daily Star Sunday says the Dane, 26, has been snapped up from Norwegian club Aalesunds but is being described by Sir Alex Ferguson as one for the future.
With Old Trafford veteran Edwin van der Sar retiring at the end of the season, United are ready to step up their chase for their top target, Atletico Madrid’s David De Gea, 20.
Tomasz Kuszczak would then either move on or drop down the pecking order.
Van der Sar could remain at Old Trafford – but it would be in a consultancy capacity on the goalkeeping front.
On the goalkeeping situation at United, Sir Alex Ferguson said: “We are looking at a lot of things at the moment.”
Shay Given is also being linked with United but agreeing a deal with neighbours Manchester City would be difficult.
De Gea is the most-wanted keeper in Europe. He has a buy-out clause in his contract of £35m but a more-realistic fee is likely to be £20m.