The Portugal international has been with Wolves for the past six years, but it is anticipated that he will leave the club.
His current contract will expire in just over a year, and according to Football Insider, the 26-year-old has no intention of extending it.
Neves has a desire to join Barcelona this summer, but as things stand, manager Xavi Hernandez is not particularly interested in him.
Therefore, Neves might have to explore other options, and there are reports that the Merseyside outfit are closely monitoring his situation.
Liverpool have been interested in Neves for a long time, and their initial interest dates back to when Wolves gained promotion to the top flight.
Rumours linking the Portuguese to Liverpool have persisted over the years, and there is a possibility that they could finally secure his signature in the summer transfer window.
Considering Wolverhampton Wanderers’ Financial Fair Play issues, it is unlikely that they would allow Neves to leave for a low fee. They could demand a minimum of £40m for his transfer.