The Premier League and La Liga sides are currently preparing for the upcoming summer transfer window after disappointing campaigns in their own rights.
While Wolves went from European qualification candidates to a 14th-placed finish in England's top flight, Atletico suffered 10 defeats and finished 19 points adrift of champions Real Madrid in Spain's equivalent.
As a result, both clubs are each scouring the market for some shrewd additions when they do not necessarily have the transfer funds to splash the cash.
Strengthening their options in the final third is a priority, either because of a lack of depth or the need to improve on their attacking numbers from 2023-24.
Braga winger on Wolves, Atletico radar
According to X account Esto Ee Atleti, and widely reported elsewhere, Wolves and Atletico are going 'head to head' for the signature of the Braga winger.
The 20-year-old has just spent the season on loan at fellow Portuguese top-flight club Estoril Praia where he contributed seven goals and seven assists from a variety of positions.
Twenty of Gomes's 30 appearances came from a wing-back position, with the others coming from right-back, attacking-midfield and on the flank.
Although it has bene indicated that Atletico are the favourites, Wolves are allegedly prepared to match or better any proposal from Diego Simeone's side.
There have been suggestions that it may take a fee in the region of £12m to get a deal over the line.
Why Gomes would suit both clubs
Possessing versatility in a squad has rarely been so important in the modern-day era when clubs are scrambling to meet the various financial rules.
Nevertheless, in this instance, it would be an astute piece of business from either side courtesy of their preference to play with a back three.
In Wolves' case, an alternative may be required for Rayan Ait-Nouri, while Matt Doherty is increasingly likely to drop down the pecking order having made 21 outings off the substitutes' bench last season.
Atletico have a wide array of players who can be deployed at wing-back, yet they will need to start signing younger players at some stage with the vast majority of their squad 28 years of age and older.