Neves has been linked with a move to Manchester United, but it is now questionable whether Ole Gunnar Solskjaer will make any further signings this summer.
The Wolves man could be heading abroad as Mendes is currently in Turin to meet with the Juventus hierarchy to discuss the future of Manchester City-linked Cristiano Ronaldo.
However, that is not the only matter at discussion between the Serie A club and the agent as he also wants to negotiate regarding Neves.
The super agent has, according to Italian daily Gazzetta dello Sport’s Carlo Laudisa, proposed that Juventus could swap Ramsey for Neves.
Wolves manager Bruno Lage has maintained the Midlands club are not actively looking to let go of the midfielder this summer, but signing Ramsey could tempt the side.
Neves has made nearly 180 appearances for Wolves in all competitions and has been a regular starter for the Midlands club for the past four seasons.
If the swap does happen, it would mean a return to the Premier League for Ramsey, a league where he has already amassed over 250 appearances for Arsenal.