The club are searching for a new leader following their decision to sack Mauricio Pellegrino on Monday night.
The Argentine had guided the team to just five wins in 30 Premier League matches, which has left the club one point above the relegation zone.
"They need a hit man to go in there, someone with the experience of being down there in the league, somebody who can get immediate results," Neville told Sky Sports News.
"It's not an exact science, we've seen it work at clubs this season, we've seen it fail at clubs this season, and previous seasons."
Southampton have eight matches left to play before the end of the campaign.