Solskjaer sought after by Rosenborg
The 36-year-old made more than 200 league appearances for the Red Devils from 1996-2007, netting 91 times, as well as scoring the last-gasp winning goal in the 1999 Champions League final.
Solskjaer - a former Norway international who won 67 caps - retired from the game in August 2007 due to ongoing knee problems, but has remained at the club in a coaching capacity, taking charge of the club's reserves a year later.
The former striker - nicknamed the 'Baby-Faced Assassin' - has already been offered the Norway job during his short coaching career, but turned it down in order to continue his development at United.
However, with current Rosenborg coach Eric Hamren the favourite for the vacant Sweden post, the 21-time Norwegian Premier League winners are believed to want Solskjaer to succeed him.
And Jim Solbakken, Solskjaer's advisor, has admitted that interest in the the former front-man's services from his homeland is inevitable.
"It is only natural that the Norwegian club would check out Ole Gunnar’s situation," he said.
"He will not be reserve team coach at Manchester United for the rest of his life."