The club finished eighth in the Premier League previous year and reached the final of the League Cup.
The 46-year-old Pellegrino joined on a three-year deal in June last year, weeks after leaving Spanish team Alaves.
"Some moments we managed this, some moments we couldn't, but we have been living a hard season for many reasons".
Alex Apati of Ladbrokes said: "Southampton will have to act quick to save their season and the early signs point towards a swift Prem return for Hughes".
As reported by The Scotsman, Celtic manager Brendan Rodgers' achievements in his first two seasons in Glasgow have lead to some strong interest from Premier League club Southampton.
Girl student stabbed to death outside Chennai college
Ashwini, studying in the first year at Meenakshi College was taken to a private hospital for stab injuries but she died later. The 24-year-old was on the way to work when an assailant, suspected to be Ramkumar, hacked her to death in the busy station.
"The club will look to appoint a new management team as soon as possible", the club said in a brief statement, "with the search for a replacement already underway".
Club chiefs will want to make an appointment quickly with an FA Cup quarter-final against Wigan on Sunday.
Like Hughes, Silva was sacked by a Premier League club in January - in his case Watford - and he has also been linked with a move back home to Portugal to take over at Benfica next season.
However, last night the Southampton board finally made a stand, sacking the man who has won just five of his 30 league games in charge.
The Welshman, who has also taken charge of Manchester City, Blackburn and QPR, played 52 league games for Saints in the late 1990s.