The two Midlands outfits have endured contrasting seasons so far, Wolves moving to make a change on Sunday with Gary O'Neil being removed from his position as head coach.
As well as there being the obvious need for Wolves to add at least one physically-imposing centre-back to their ranks in January, Forest are also of the mindset that further fresh faces could boost their efforts to qualify for Europe.
According to The Sun, both clubs have identified Godfrey as a player who could be a difference-maker from January onwards.
Frustrating Serie A spell
Having spent time out of the Everton XI under Sean Dyche, Godfrey jumped at the opportunity to take on a new challenge with Atalanta in the summer.
The expectation was that the two-cap England international could be provided with regular game time during his stint at the Gewiss Stadium.
Instead, Atalanta's Serie A title charge has contributed to Gian Piero Gasperini being reluctant to tinker with his backline when it is not necessary.
Therefore, Godfrey has been restricted to just 22 minutes of Serie A football, a further two outings coming as a substitute in the Champions League.
With just 66 minutes to his name all season, the report suggests that the 26-year-old is ready to push for a transfer away from Atalanta in January.
As it stands, it is unclear whether La Dea would be prepared to part ways with Godfrey, who cost in the region of £10m just six months ago.
Wolves to hold the advantage?
If Godfrey is eager for first-team football, it would make sense to move to Wolves, regardless of their plight at the bottom end of the Premier League table.
There will be at least one opening for a new centre-back to slot straight into the club's defence upon their arrival at some point in January, there seemingly being the likelihood that Vitor Pereira will be appointed as O'Neil's replacement.
At Forest, Nuno Espirito Santo already has Nikola Milenkovic and Jeison Murillo as his standout partnership in the middle of the backline, leaving Godfrey with the prospect of more substitute appearances if he were to move to the City Ground.
Written by
Darren Plant