The Portugal international has again been a key player for his English club during the 2021-22 campaign, making 35 appearances in all competitions, contributing four goals and two assists in the process.
Neves only has two years left to run on his current deal, though, and there has been a host of speculation surrounding his future over the last few months.
Manchester United and Arsenal are among the clubs to be credited with an interest in the midfielder.
However, talk of a switch to Camp Nou has grown in recent weeks, with Barcelona boss Xavi said to be determined to boost his midfield during this summer's transfer window.
According to Sport, Neves's agent Jorge Mendes is currently in advanced negotiations with the Catalan giants over a move for his client in the upcoming market.
The report claims that Monaco's Aurelien Tchouameni and Real Sociedad's Martin Zubimendi are also targets, but Barcelona have identified the Wolves midfielder as the first-choice option.
Neves is allegedly aware of interest from the Premier League but is determined to complete a move to Camp Nou during this summer's transfer window.
The Portuguese joined Wolves from Porto in July 2017 and has represented the English outfit on 211 appearances in all competitions, contributing 24 goals and 12 assists in the process.
Neves was recently sidelined with a knee injury but has now featured in his side's last four Premier League matches, including Sunday's 1-1 draw with Norwich City.
Barcelona are said to be seeking a long-term replacement for Sergio Busquets, while Frenkie de Jong could leave the club this summer, with the Dutchman thought to be a target for Manchester United and Manchester City.
Pedri is said to be one of the 'untouchables' at the club, but Nico Gonzalez could potentially leave on loan, while Riqui Puig is also being linked with a summer exit.
Gavi, meanwhile, is out of contract at Camp Nou next June, and the Catalan outfit are currently struggling to sign the Spain international to an extension.
Xavi's side will play their penultimate match of the 2021-22 La Liga season away to Getafe on Sunday evening before finishing at home to Villarreal next weekend.