The 24-year-old played a key role in the club's title success last season and it is understood that a host of European clubs are monitoring developments. However, Solskjaer has urged United to make a move for the central defender.
"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. Vegard is a very good footballer but he has to be focused on delivering and securing his place in the Norway team."
Molde currently top their domestic league by three points.