Villa owner Randy Lerner sacked Alex McLeish on Monday after a wretched 11 months in charge, and Solskjaer is seemingly seen by the owner as the young, progressive manager to take Villa forward.
After 11 seasons as a player with Manchester United and a further two and a half years at Old Trafford as reserve team manager, the 39-year-old returned to Molde in 2010.
Last October, at the end of his first season in charge, Solskjaer guided Molde to their first Norwegian League title in their 100-year history.