The Portugal international is admired by the likes of Manchester United and Arsenal, but neither club have made a formal bid for the Wolves star.
Neves' current club slapped on a hefty £40 million price tag on the player as interest from the Premier League clubs hotted-up in January. However, it is now understood that Barcelona have begun swooping in on the player.
The Daily Mail report that the 24-year-old is likely to leave the club this summer, and talks involving intermediaries have taken place concerning Barca's interest.
The 24-year-old's now former teammate Traore secured a short-term move to the Nou Camp thanks to Neves' agent, Jorge Mendes, back in January.
It's been reported the Wolves loanee could make the deal permanent come the summer, and Neves could well follow suit.
The Wolves cult hero was heavily linked to a move to Old Trafford in January and last summer, and the midfielder has since come out and stated his focus is still on his time at Molineux. However, he did not rule out the possibility of moving elsewhere in the future.
"It's normal in football," Neves told Record last month, addressing the ongoing speculation.
"Whenever there's a transfer market there's a lot of talk, but my goal and focus are on Wolverhampton and I'm not going to change that, things have been going really well for me.
"…But in football, the future is very uncertain and we don't know what will happen. Obviously, I'm curious to see other championships, but I definitely like being here."
Given these comments were made prior to Neves's jab at Arsenal, and United are rumoured to have put West Ham's Declan Rice at the top of their midfielder wish list, a move to Barcelona seems the more likely for Neves.
The move to the Nou Camp has worked out for other former English top flight stars, former Gunners captain Pierre Emerick-Aubameyang and now, Traore.
While a move away currently looks attractive, Wolves could well persuade Neves to stay until the end of his current deal.
The Midlands outfit are still battling it out for a top six or top four finish, and Neves may not require a big money move to play against football's best.
The 24-year-old joined from Porto in 2017 and quickly established himself as a fan favourite.
He helped the club win promotion to the Premier League in his first season and has amassed 203 appearances, scoring 23 times.