The coastal club announced the dismissal of the Argentine on Monday evening.
The club sit just one point above the relegation zone in the Premier League following just five wins in 30 top-flight matches.
Savage thinks that Hughes, who has been out of work since getting sacked by Stoke City in January, would help Southampton in the final stretch of eight games.
"You might think I'm mad but with eight games to go and looking at men who are out of work - it's Mark Hughes," the pundit told BBC Radio 5 live.
"He has never been relegated as a Premier League manager. He played for Southampton, and he will want to prove Stoke wrong. He has lots of experience."
Reports have claimed that the Saints want a new manager at the club before Sunday's FA Cup quarter-final.