The story has also been repeated by the Daily Mail.
The article alleges that the Saints hierarchy have already drawn up a shortlist of potential replacements, with Fulham’s Slavisa Jokanovic and Ostersunds FK manager Graham Potter, the latter of whom had a brief spell at Southampton as a player in the ‘90s.
Jokanovic has led Fulham to an impressive mid-season run in form to firmly embed the West London side in the Championship playoff positions.
Meanwhile, Potter has achieved the near-impossible with Swedish minnows Ostersunds, taking them from the fourth tier of Swedish football to the top division - Allsvenskan - as well as a place in the Europa League group knockout rounds.
Ostersunds defeated Turkish giants Galatasaray over two legs to earn their spot in the competition and Potter saw his team defeat Arsenal 2-1 away at the Emirates in the round of 32 this season.
Pellegrino hasn’t exactly set the world on fire while overseeing Southampton as head coach, winning just five Premier League games from 29.
According to the report, Saints’ Vice Chairman Les Reed is “reluctant to make a change before the summer and risk a panic appointment.”