Hughes has taken charge of almost 450 Premier League matches for Blackburn, Manchester City, Fulham, QPR and Stoke.
The Argentine manager came to England after a fairly successful run with Spain's Alaves, but Southampton sit 17th in the EPL, just one point above the relegation zone with eight matches to play, reports Efe.
He eventually left the club in the summer, supposedly to retire, but ended his self imposed retirement to help Everton, who were flirting with the relegation zone, back in November of this season.
The 46-year-old arrived at St Mary's as the replacement for Claude Puel, who was sacked despite guiding Southampton to an eighth-placed finish and the League Cup final.
Saints will be hoping to appoint Pellegrino's successor quickly, with an FA Cup quarter-final at Wigan looming on Sunday.
Journalist Jeremy Wilson has claimed that Silva is not in the frame and that Southampton are on the lookout for a manager - with Premier League experience - in by the weekend.
Assistant manager Carlos Compagnucci and assistant first-team coach Xavier Tamarit have also parted company with the south coast club.
As The Guardian wrote at the time, Puel "did not fall short of the reasonable expectations that Southampton could have had when they appointed him less than a year ago, he just failed to meet their admirably unreasonable ones".
President Trump meeting with North Korea could bring temporary p
Some experts are concerned that North Korea could be seeking to delay worldwide action while strengthening its nuclear program . North Korea is a dictatorship and an impoverished country, crippled by a failed economic system and harsh worldwide sanctions .
Buhari's visit: Security beefed up in Makurdi
Benue State has been at the centre of the Fulani Herdsmen crisis, recording more than 120 deaths in 2018 alone. And I didn't know he moved here (Benue State) and didn't spend (time) and then move to Nasarawa.