The former Manchester United striker has received enquiries about his availability, but the Norwegian side would not reveal where the offers have come from for their coach
Former Manchester United striker Solskjaer scored 126 goals in 366 appearances for the English giants before returning to his native Norway.
Since taking over at Molde in 2011, Solskjaer has led the side to two league titles and they won the Norwegian Cup against Rosenborg in November.
The 40-year-old has been strongly linked with the recently vacant positions at Premier League clubs West Brom and Tottenham, and managing director at Molde, 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.
"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."