Sunderland saw boss Dick Advocaat leave his post on Sunday following a 2-2 draw with West Ham United, meaning owner Ellis Short must now press ahead with his search for a new manager.
The current favourite with the bookmakers is former Sunderland defender Sam Allardyce, who is a free agent having left West Ham United at the end of last season, whilst caretaker manager Robbie Stockdale will be looking to earn a chance himself.
Mazzarri, 54, made his name in Italy during successful spells with Sampdoria and Napoli, and whilst he didn't enjoy much success in his last job with Inter Milan, he remains a highly-rated manager.
However, it doesn't appear that Mazzarri will be moving to the Premier League any time soon, with the same report also stating that Mazzarri has had no contact with Liverpool over their managerial vacancy.
The Reds parted company with Brendan Rodgers on Sunday evening, leaving both them and Sunderland to consider their next moves - though neither will seemingly be landing Mazzarri.