The London side have made contact with Wolves to express their interest in signing the midfielder this summer.
But while early talks have been held, a transfer is only likely to take place if the Gunners can sell some of the players on the fringes of their squad.
Neves was one of Wolves’ star signings when Nuno Espírito Santo first took charge of the club back in 2017.
In his first season at Molineux, the Portuguese midfielder helped the club win promotion to the Premier League.
He has since gone on to feature in 109 top flight games and is currently away with the Portugal squad as they look to win back-to-back European Championships.
But with Nuno having now departed and with Bruno Lage imminently expected to be announced as the club’s new boss, Wolves are believed to be willing to listen to offers for certain players to help fund a summer rebuild.
With Raul Jimenez and Pedro Neto both on the recovery trail after picking up serious injuries, Neves and Adama Traore and currently the club’s most saleable assets.
And Arsenal have now made their interest in Neves known – with the Gunners hoping to strike a deal if they can offload fringe midfielders including Granit Xhaka and Ainsley Maitland-Niles.
Wolves cashed in on both Diogo Jota and Matt Doherty last summer to fund moves for Fabio Silva and Nelson Semedo.
And in order to generate more funds, other members of the squad have recently been linked with moves away.
Roma – now managed by Jose Mourinho – are believed to be keeping tabs on goalkeeper Rui Patricio – whose contract at Molineux expires in 12 months time.
Midfielder Joao Moutinho has also been linked with a move to Porto amid claims he is ready to return to his homeland.