Having spent the past five years at Molineux, it has been widely speculated that the West Midlands outfit will consider selling their most prized asset this summer.
That suggestion was backed up by Neves's own comments on the final day of the season, the 25-year-old saying that "we need to take the opportunities we have".
At the time, that was seemingly in relation to interest from Barcelona, who had previously been suggested as Neves's preferred destination should he leave Wolves.
However, The Sun says that the Portugal international is now likely to spend another year at his current club.
The report claims that Barcelona, Manchester United and Arsenal have all been put off by Wolves' alleged asking price of £75m.
In sharp contrast, the three clubs mentioned are seemingly only prepared to pay in the region of £45m, inevitably leading to an impasse in negotiations.
As it stands, Barca, United and the Gunners are yet to sign an alternative to Neves, although the former two sides are said to be negotiating the transfer of Frenkie de Jong.
That would theoretically provide Barcelona with the funds to put together a proposal for Neves, but the La Liga giants will first look to finalise the free transfers of Andreas Christensen and Franck Kessie as they continue to deal with financial issues.
If, as reported, Neves spends the 2022-23 campaign at his current club, Wolves will almost certainly look to agree a new contract in a bid to retain his valuation.
Such a development would also represent a significant boost at a time when Wolves appear to have lost out to Fulham in the race to sign Sporting Lisbon midfielder Joao Palhinha.
Matheus Nunes - another Sporting midfielder - is yet to decide whether to move to Wolverhampton, while it is increasingly unlikely that Bruno Lage will hang onto Joao Moutinho.
The Daily Mail said on Wednesday that Wolves were not prepared to offer the 35-year-old a contract through to the end of the 2023-24 campaign, instead insisting on a 12-month deal.
Although remaining senior midfielder Leander Dendoncker has just one year left on his contract, Wolves have the option of extending the Belgian's contract until 2024.