The 20-year-old Norwegian has played only one senior game for the Red Devils after graduating from the club's youth academy in 2010.
"I have set Christmas as a deadline." King told VG. "If I haven't got more playing time by then, I will consider moving to another club.
"Considering the players United have, it is not easy to get into the starting XI.
"I would prefer to stay in England, but in case I do return to Norway, Molde is the only option."
King has had loan spells with Preston North End, Borussia Monchengladbach and Hull City in recent seasons.