talkSPORT understands the Welshman is the south coast club's number one choice to succeed Mauricio Pellegrino.
Pellegrino was sacked on Monday after the 3-0 defeat at Newcastle on Saturday left the Saints just one place and one point above the Premier League relegation zone.
With just eight games left of the season, Southampton want to appoint an experienced Premier League boss and Hughes fits the bill.
Southampton are keen to appoint Pellegrino's successor quickly too, with an FA Cup quarter-final at Wigan looming on Sunday before a crunch clash with relegation rivals West Ham at the London Stadium on March 31.