According to Sportitalia, former Milan and Torino Coach Mihajlovic has received a call about the role.
Premier League survival is the main aim but whoever takes over could well be just 180 minutes from leading Saints to a major cup final. They also need to contend with the FA Cup, where they face Wigan Athletic in the quarter finals.
Mark Hughes, until his sacking in January the manager at struggling Stoke, is the present bookies' favourite to be appointed.
Southampton, who are the ninth Premier League club to change manager this term, are in their sixth straight season in the top flight and have not finished lower than 14th in that time.
Pellegrino, the 46-year-old Argentine, was dismissed from his position at St Mary's on Monday evening, on the back of just one victory in 17 league matches.More news: Castro trusts his team's ability to defeat Man United
Former Stoke City boss Mark Hughes - who had a stint with Southampton during his playing days - has now been cut to just 1/6, making him nearly nailed-on to become Pellegrino's replacement.
Southampton were thrashed 3-0 by fellow strugglers Newcastle at the weekend and head to embattled West Ham on March 31 in their next Premier League match.
"From the beginning I tried to do my best every single day", Pellegrino said in a statement published by the club.
"I feel so sorry to leave the club in this situation, but when you don't get results I understand the decision the club has to take", he said.
Hughes played for Saints between 1998 and 2000 and they believe that he has the experience to steer the club away from the relegation zone.
The Welshman most recently managed Stoke City before being sacked earlier this season, having been boss for a lengthy five years.