Solskjær is currently manager of Norwegian top flight club Molde (MFK) and the club have confirmed that Aston Villa have made an approach for the 39-year-old, according to a report in the local Romsdals Budstikke newspaper.
"The management of MFK became aware of interest from Aston Villa around two and half days ago," said Tarje Nordstrand Jacobsen to the newspaper.
According to Norwegian media reports Molde are open to the idea of negotiating with the Premier League club which narrowly avoided relegation after a disastrous campaign by their standards and prompting the sacking of manager Alex McLeish.
According to the Verdens Gang (VG) daily, US magnate and Villa owner Randy Lerner's private jet landed in Kristiansund in southern Norway late Thursday night, carrying a team of Aston Villa officials.
Solskjær represented Manchester United for 11 years, winning a slew of trophies and earning the nickname "the baby-faced assassin" for his knack of scoring crucial goals as a substitute.
His defining moment as a player perhaps came already in the 1999 Champions League final, scoring the winner in a dramatic injury-time win over Bayern Munich.
After injury cut short his career at the English club, Solskjær returned to his first club Molde, signing a four-year contract to manage the Tippeligan team. The amiable Norwegian enjoyed instant success at the helm, guiding Molde to their first ever league championship title in October 2011.