Originally linked with the role when Lambert's future first came into question, Karanka helped guide Middlesbrough to the Premier League before getting the boot late on in their immediate drop back to the second tier.
He's a client of Jorge Mendes and does have experience at the Championship level, but his record last season may raise some eyebrows among fans.
A recent Express & Star poll stated that almost two thirds of voters didn't want Karanka appointed at Molineux.
Looking for a way back into management, Pearson originally masterminded Leicester City's Premier League survival before getting the boot ahead of their miraculous title-winning season.
Often credited for his role at the King Power, a short stint at Derby followed before leaving in questionable circumstances.
Appearing on Sky's Goals on Sunday this month, he confirmed that he was willing to head back into management, being heavily linked with the Middlesbrough job.
A man held in high regard despite seeing his Hull City side relegated from the Premier League.
Silva was originally linked with the Wolves job following Kenny Jackett's departure in the early days of the Fosun reign.
His work with Hull was a clear indicator of a talented manager, so much so that he may hold out for a job in the top flight or elsewhere in Europe.
Another former Derby boss, but one not held in the highest regard since his infamous stint as England manager.
McLaren does have a wealth of experience on the continent though, helping lead FC Twente to the Eredivisie title and taking the top job at Wolfsburg.
His latest Premier League spell with Newcastle left a lot to be desired though, and given his recent failings at Derby too he wouldn't be the most inspiring name to replace Lambert.
A big name on the list, but less likely to make the drop into the Championship, Alan Pardew has recorded stints with Southampton, Newcastle and most recently Crystal Palace.
Known for trying to play an expansive style of football, Pardew would certainly offer a different personality to that of Paul Lambert.
Not without his controversies, the 55-year-old is known for his fiery temperament, previously headbutting Hull City player David Meyler during his spell in charge of Newcastle United.
Likely to split opinion.
What an appointment this would be, albeit incredibly unlikely.
Ranieri was the man who guided relegation candidates Leicester City to the Premier League title. If he can do that, surely he can help Wolves to promotion, right?
A real character, his CV boasts big names including Chelsea, Inter Milan, Monaco and Juventus - taking the role at Molineux would be a real surprise.
Formerly working alongside Sir Alex Ferguson at Manchester United, Phelan helped lead Hull City's surprise start to last season, claiming the Premier League Manager of the Month award for August 2016.
However, following a torrid mid-season run, Phelan was eventually replaced with Marco Silva at The KC Stadium as they attempted to secure survival.
A renowned coach, but with a questionable managerial record, bringing him in might be seen as a sideways or backwards step from Paul Lambert.
Still looking for his first permanent job in management, Giggs has experience from his spell in charge of Manchester United following David Moyes' sacking in 2013.
The Welshman was heavily linked with the permanent job following Louis Van Gaal's exit, but as the club hired Jose Mourinho he decided to move on.
His lack of experience will deter many fans, and given the high pressure environment at the club to secure a playoff spot and ultimately promotion it may be a case of too much too soon.
Not likely to be the first name on many Wolves fans lips if Paul Lambert leaves the club, Roger Schmidt was in charge of Bayer Leverkusen up until March this year.
Sacked following a 6-2 loss to Borussia Dortmund, the former midfielder is well-known in Germany for holding up Leverkusen's previous fixture against Dortmund this season for over eight minutes after getting sent off.
Clearly a hot-headed customer, bringing in the German would be a surprise.
The man currently in charge of Sheffield Wednesday, he helped lead the Owls to the playoffs before being defeated by Huddersfield Town on penalties.
The Portuguese former defender has plenty of experience in management too, with spells at Besiktas, Sporting CP and Braga amongst others.
His knowledge of the Championship will also be very beneficial if he does take over at Molineux, although prising him from Wednesday will be tough.