Ex-Watford boss Marco Silva and former West Ham United head coach Slaven Bilic are the other frontrunners in the betting to take over at St Mary's Stadium. Click the right arrow above to see who the favourite is, according to SunBet odds...
Southampton managed only one win in Pellegrino's last 17 Premier League matches at the helm, sliding to fourth from bottom in the table, one point above the relegation zone. As for Puel, he is now in charge at Leicester who, ironically, are eighth in the Premier League, the position that Saints were when they fired the Frenchman.
With the form Southampton have been in this year, Pellegrino's sacking has been more of an inevitability than anything else, but with only eight matches left in the season, it puts the club in an incredibly hard position.
Real Madrid beat Eibar 2-1 in La Liga
A Cristiano Ronaldo double was enough for Zidane's side who remain third and 15 points behind Barcelona who face Malaga tonight. But Ronaldo proved the difference again, the 33-year-old taking his tally for the season to 35 goals in 37 appearances.
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".
The club said it wants to "appoint a new management team as soon as possible, with the search for a replacement already under way".
It is believed Southampton aren't set to appoint Hughes imminently, while other candidates such as former Hull City and Watford manager Marco Silva, plus ex-West Ham boss Slaven Bilic, aren't now in the running.
Former Alaves coach Pellegrino did lead the south-coast club into the FA Cup quarter-finals, with the now-managerless side set to visit third-tier Wigan in the last eight on Sunday.