The former Manchester United striker has been linked with previous vacancies in the Premier League - with West Brom the most recent - and the club are prepared for an exit
Since taking over at Molde in 2011, the former Manchester United striker has led the side to two league titles and they won the Norwegian Cup against Rosenborg last month.
The 40-year-old has been linked with the vacant positions at West Brom and Tottenham, and Molde managing director, Tarje Nordstrand Jacobsen, admitted several clubs were keen on speaking with Solskjaer.
"I can confirm that we have received formal requests, but will not say when they arrived or where they came from," Jacobsen told Norwegian newspaper Romsdals Budstikke.
"Ole has a name and a location that will always make him attractive. And he has a standing in England that makes him often be a candidate there."
Solskjaer's contract at Molde is up midway through 2014 and Jacobsen said he has been in regular contact with the coach - who is keen on a resolution before Christmas, and are prepared for a possible departure.
"We asked for a clarification before Christmas," he added. "We talk daily, but do not [know] yet when this will be settled.
"We are aware that there is a possible scenario [where Solskjaer leaves the club].
"Ole has won three titles in three years in Molde. It is obvious that this can be good timing for him if he wants to further his career."