For a number of months, it has been suggested that the Catalan giants were the frontrunners to sign the Portugal international, who has publicly acknowledged that he is open to considering offers from elsewhere.
However, Barcelona's financial issues have prevented any deal from moving forward, while Wolves have insisted that they will not part ways with Neves for a cut-price fee.
According to Sport, club officials are now ready to shelve their interest in signing for the 25-year-old until next year.
The report suggests that Barcelona intend to try to take advantage of Neves only having one year remaining on his contract at Molineux in 2023, providing that nothing changes on that front.
Last month, it was claimed that Wolves would look to extend Neves's deal past 2024 should they successfully retain the services of their most prized asset.
The outlet says that Barcelona feel that the player will be available for €40m (£34.7m) if they show patience in their attempts to conclude the transfer.
The La Liga side had attempted to include at least of their fringe players in a bid to drive down the financial outlay for Neves, only for Wolves to stand firm with their demands.
At a time when Wolves are yet to make any first-team signings, Neves's compatriot Joao Moutinho technically became a free agent on Friday.
The veteran is still believed to be in negotiations with Wolves officials, although they are yet to show a willingness to offer the 35-year-old terms until 2024.
However, while Palhinha is said to be on the brink of signing for Fulham, a club-record bid for Nunes may have to be shelved if Wolves do not recoup the funds that they were expecting from the exit of Neves.
Wolves may look to engineer the departure of Adama Traore to generate a bigger transfer budget for Bruno Lage, the winger having no intention of extending his contract past the end of 2022-23. body check tags ::