The Toffees are engaged in the hunt for a new manager after showing Rafael Benitez the door and have interviewed several candidates.
Italy legend Cannavaro is one of the candidates that Everton chose to hold talks with, but it is claimed he now does not have a large chance of taking over.
Cannavaro is keen to become the new Everton boss, but it appears the club will go in a different direction to the Italian.
Everton have also spoken to former FC Porto and Fenerbahce coach Vitor Pereira, and he is now claimed to be a strong contender to take charge at Goodison Park.
Duncan Ferguson is currently leading the club as caretaker boss and his reign got off to a losing start at home against Aston Villa.
Everton are only four points above the relegation zone in the Premier League and have lost eleven of their 20 games.
They are in FA Cup action next with a home tie against fellow top flight club Brentford.