The former Manchester United striker has enhanced his coaching credentials with back-to-back titles in his native Norway, the club's first ever in their history.
That success and a failure to extend his current contract, which expires in 2014, has seen him linked to various vacancies, with his name now heading the list of candidates to replace Steve Clarke at 11/8.
Molde director Tarje Nordstrand Jacobsen told Norweigen newspaper Romsdals Budstikke: "I can confirm that we have received formal requests, but will not say when they arrived or where they came from."
Gianfranco Zola had led the market following his departure from Watford but has now drifted out to 4/1 second favourite, followed by Malky Mackay (6/1) amid uncertainty over his position at Cardiff.
Solskjaer is also considered in the betting for the next Tottenham manager but is an outsider at 33/1, with Frank de Boer and Tim Sherwood the current favourites.
Sky Bet's Chris Spicer said: "We have seen a significant run of bets for Solskjaer to get the job, noticeably since it was confirmed that Molde have received approaches.
"Since moving on from his role with the academy at Old Trafford to achieve unprecedented success in Norway, he has been touted as a future Manchester United manager and West Brom looks the ideal platform to enhance his credentials further."