Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The 38-year-old held discussions with Ajaccio - now managed by his former Juventus team-mate Fabrizio Ravanelli - concerning a move but will instead remain with Sydney FC in the Australian A-League.
A statement on the Ajaccio website read: "For several weeks the club have been in discussions with the celebrated Italian forward Alessandro Del Piero.
"Aged 38 and currently a player with Sydney FC, he will not ultimately come to Ajaccio. After reaching an agreement in principle, family reasons persuaded him to stay in Australia."
Del Piero spent almost 20 seasons as a professional with Juventus, scoring over 200 goals, before moving to Sydney last year. He won 91 senior caps for Italy, scoring 27 goals.