The Norwegian only took charge at Molineux in the summer but had presided over a terrible run of form with a cup defeat to non-league opposition proving to be the final straw for the board.
Sky Bet swiftly installed Saunders as odds-on favourite to take over, though the League One side later took to Twitter to declare that they had received "no official approach".
Wolves are on a run of just three wins from 17 games and, far from challenging for an immediate return to the top flight, they are in danger of slipping into relegation trouble.
The Midlands side are 18th in the Championship at present, six points clear of the drop zone.
Wolves confirmed in a statement that Solbakken, assistant manager Johan Lange, and first-team coach Patrick Weiser had all been dismissed.
The statement added: "Wolves have won three out of the last 16 league games after a hugely disappointing run of performances and results, culminating in Saturday's FA Cup third round defeat to Luton Town.
"Kevin Thelwell, Head of Football Development & Recruitment, will take charge of first team training until a new manager is appointed, assisted by Development Coach, Steve Weaver.
"The club would like to offer their thanks and best wishes to Stale, Johan and Patrick. Wolves will be making no further comment to the media at this current time."
Speaking after the Luton defeat, Solbakken said: "There will be a lot of questions over me but that is normal. That's football and I have to take that, it's no problem. I can put it right."
But Wolves bosses have decided to go in a different direction and the club are now seeking a fourth manager in less than a year, after the dismissal of Mick McCarthy last February and the short reign of Terry Connor.