Marcelo is out of contract in 2022 but the 33-year-old Madrid left-back is facing an uncertain future with the LaLiga giants due his form and advancing years.
Inter Miami, who are co-owned by former Madrid star David Beckham, have emerged as an option for Marcelo – ex-Los Blancos forward Gonzalo Higuain and World Cup-winning midfielder Blaise Matuidi headline the squad.
Current Madrid captain Sergio Ramos, who is set to become a free agent at the end of the season, is also reportedly on Inter Miami's radar.
However, Neville poured cold water over the speculation linking Brazilian veteran Marcelo with Inter Miami.
"I don't need another left-back," ex-Manchester United utility Neville told reporters. "I've got more left-backs than yellow taxis, you know what I mean. We could do with a few more positions but no.
"I think it shows the level of the club and interest in the club, yes. But ultimately, I think what I want for us is pure stability. So when they have all these stars that are being linked with Inter Miami it's brilliant, shows that the people do want to come to Inter Miami.
"But ultimately, I want us to have stability here, I want players to be here for a long time. You think about every time somebody gets mentioned, somebody in this football club, somebody in this team, in my team will feel, even if it's point one percent unnerved by it, that's not good for us, it is not good for the player.
"What I would say is, and I and Chris Henderson talk about this all the time, is that the most successful teams, you think about the Seattle team, Chris Scott first and experience of it, stability is the key. The great team that I played in Manchester United, you had the core of a team that was together for four or five years before Sir Alex [Ferguson] rebuilt it.
"Yes, you sprinkle around the edges and you tweak here and there you introduce new players around the edges, but you're gonna have eight, nine players that are going to be here for the next three or four years to get that stability and I'm talking about the DP [designated] players as well they need stability. You know the worst thing that can happen is them reading the newspaper every single day thinking about who's coming to the club.
"We believe in the players that we've got, we've, the ownership have invested so much money in this football team. And now I think stability is the only way we'll get success that's what the best team in this league have had that's what the best teams in football, have had success on, stability.
"We're never going to stop you guys speculating and, you know, an agent's putting in players because this is a place that a lot of players will want to come, but ultimately I'm happy with the squad that I've got, I want stability around this place."
Marcelo has called Madrid home since 2007, winning five LaLiga titles and four Champions League trophies among other honours.
Meanwhile, Inter Miami – into their second MLS season and first under Neville – have won two of their opening six matches to sit seventh in the 14-team Eastern Conference.