The Molde FK manager has suggested the young Norwegian could join the Red Devils, but also warned him to remain focused on securing his place with the national side
Solskjaer led the Norwegian side to their maiden league title last season, generating a great deal of speculation about his own future and whether a return to England could be on the cards.
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However, the 39-year-old has instead suggested that defender Forren, 24, could make the move to Old Trafford before long.
"Yes, he could play for Manchester United, but I don't have to tell him that. At his best he is a very good footballer," he told TV2.
"He could play for United, but he doesn't need me to tell him that.”
Despite his kind words, the Norwegian went on to warn Forren that he should keep his attention focused on his own burgeoning international career.
"Vegard is a very good footballer but he has to be focused on delivering and securing his place in the Norway team," he continued.
Molde currently sit top of the Tippeligaen, three points ahead of the pack with three matches still to play.