The Saints were enduring a torrid spell under the Argentine, with just one win coming in their last 17 Premier League games.
Assistant manager Carlos Compagnucci and assistant first-team coach Xavier Tamarit have also parted company with the south coast club.
Silva impressed many with his ultimately fruitless attempts to guide Hull City to Premier League safety past year and he made a good start at Watford this season until an approach from Everton soured his relations with the club.
Hughes played more than 50 times for Southampton in the late 1990s and his appointment would end a run of four non-British managers after Mauricio Pochettino, Ronald Koeman, Puel and Pellegrino.
"There are all sorts of managers mentioned; Mark Hughes has a lot of Premier League experience and I think that will count in his favour".
Southampton are not thought to be planning a swoop for Marco Silva as they eye up a replacement for the sacked Mauricio Pellegrino.
Saints will be hoping to appoint Pellegrino's successor quickly, with an FA Cup quarter-final at Wigan looming on Sunday.
Some observers were surprised when Southampton fired manager Claude Puel last summer after he guided the team to an eighth-place finish in the EPL and to the final of the EFL Cup, where they lost 2-3 to Manchester United.
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