Antonio Conte is expected to leave the north London club at the end of the season when his contract expires.
The Italian could even leave earlier if Spurs’ top-four chances start fading away.
Levy is already preparing for life without the former Chelsea boss.
Ex-Spain manager Luis Enrique and Brighton & Hove Albion boss Roberto De Zerbi have also been linked.
A return for Mauricio Pochettino has also been mooted, but Tottenham have a list of potential alternative targets.
Spalletti is impressing with Napoli after guiding them to the top of Serie A.
The Italian club are 15 points clear of Inter Milan after 25 games and are huge favourites to win their first Serie A title since 1990.
Spurs have not won silverware since 2008 and could do with such a manager.
Spalletti could finally win his first Italian top-flight title, and his huge experience would come in handy.
Postecoglou also brings plenty of experience and quality to the table.
The Australian won trophies managing his country, South Melbourne, Brisbane Roar and Yokohama F. Marinos.
He joined Celtic in 2021 and has won two Scottish League Cups and a Scottish Premiership title.
The Hoops boss knows one or two things about winning silverware, and Tottenham need someone like that.
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