His contract at Molineux is due to expire next summer and the midfielder had been heavily linked with a move to Barcelona this summer.
However, it appears Al-Hilal have stolen a march on other potential suitors for Neves after talks with Barça's representatives allegedly stalled.
Personal terms are yet to be agreed but are not expected to pose a problem for the club or player.
Neves will join a growing list of stars heading to the Middle East to ply their trade, with Cristiano Ronaldo recently being joined by former Real Madrid teammate Karim Benzema and the likes of Angel Di Maria, N'Golo Kante, Hakim Ziyech and Pierre-Emerick Aubameyang all expected to join the Saudi Pro League in the coming weeks.
But while those players are respectfully in the 'twilight' of their careers, Neves' transfer stands out somewhat, with the player still seen as being very much in his prime.
Neves scored six goals and registered one assist in his 35 Premier League appearances for Wolves during the 2022/23 Premier League season.
He joined the club from Porto in July 2017 and has turned out 253 times for the club.