The West Midlands outfit have been proactive in the transfer market of late, completing big-money deals for Goncalo Guedes and Matheus Nunes.
However, head coach Bruno Lage has not been shy about acknowledging that he still wants to make more additions to his first-team squad before the start of September.
Wolves are known to be interested in signing Stuttgart forward Sasa Kalajdzic, who is said to be open to making the switch to Molineux.
According to the Daily Mail, Lage also has his sights set on bringing in Nelson from Galatasaray over the coming days.
Nottingham Forest are looking to sign third-choice centre-back Willy Boly with the Ivory Coast international having less than 12 months remaining on his contract.
Although Forest are yet to agree a deal with Wolves, the two clubs are said to be in dialogue with Boly likely to be sold over the coming week.
That would free up a slot on Lage's defensive ranks with Nelsson seemingly at the top of Wolves' shortlist with regards to a replacement for Boly.
In 12 months at the Turkish giants, Nelsson has made a total of 47 starts in all competitions, the 23-year-old currently regarded as a key part of the backline.
With four years still remaining on his contract, Galatasaray will be in no rush to part ways with a player who has also earned seven caps for Denmark.
Nelsson may also be against departing his current club if he is not in line to earn regular action with Wolves as he looks to secure a place in his national team's World Cup squad.
However, having paid just £6.3m for Nelsson last year, Galatasaray have an opportunity to make a considerable profit on a player who is now one of their most prized assets.
Galatasaray have collected six points from their opening three league matches this campaign, conceding just the one goal.