The former Manchester United striker resisted approaches from Aston Villa over the summer but, as he again impresses by taking MFK to the top of the Norwegian Tippeligaen, another English club are reported to be interested in him.
Blackburn lost their manager on Friday when Steve Kean ended his controversial reign and Solksjaer, still just 39, is one of the favourites to replace him.
He has a job to do with Molde on Thursday, though, with his side currently sitting bottom of Europa League Group E following an opening-day defeat to FC Copenhagen.
They have a chance of redemption against Stuttgart and Die Roten have been well briefed in what to expect from Molde.
Stuttgart's sporting director, Fredi Bobic, played against Solksjaer while a Bolton striker and knows all too well how he will set his side up.
"His style is very recognisable," Bobic told his club's official website.
"They are very good attackers, they defend well and deep and then get you on the counter-attack.
"The difficulty for us is that they (Molde) will be well trained, tactically, and they can always find space.
"This is something we are well aware of. But they are also like a rock in defence."
The sides have met in European competition before - Stuttgart edged Molde out of a Europa League play-off 5-4 in 2010.
That result still haunts some of the Molde players too, in particular Mattias Mostrom.
"I had some huge chances and should have scored more goals," said the 29-year-old winger.
"But that was not a group game, it was a qualifier. Hopefully this time the stands will be full."