The former Manchester United striker has been a revelation in his homeland since taking charge of Molde in 2011, leading them to the first two Norwegian titles in the club's history
Solskjaer has been linked with the vacant manager's job at West Bromwich Albion and, while Molde refused to name the clubs who have approached them, they have hinted at interest from England.
"I can confirm that we have received formal requests, but will not say when they arrived or where they came from," Molde director Tarje Nordstrand Jacobsen told the Romsdals Budstikke newspaper.
"Ole has a name and a reputation that will always make him attractive. And he has a standing in England that often makes him a candidate there."
If an English club did move for Solskjaer it is unlikely they would require much compensation to release him from his contract which expires in 2014.
Molde have already offered him an extension to his current deal but the 40-year-old has yet to respond.
Before becoming Molde manager, Solskjaer was in charge of Manchester United's reserve team. He had been linked with the Blackburn and Aston Villa jobs in recent years, but elected to stay in his native Norway.