The talented winger enjoyed a strong loan campaign with Rangers last term and hoped, initially, to make the comeback to North London and compete for a first-team spot.
Moore, 18, has been with the squad for pre-season and played against Auckland during their camp but head coach De Zerbi admitted at full-time that he wants to sign wide players.
That could drop Moore further down the pecking order and the Italian acknowledged that a conversation regarding the player's future is on the agenda.
Asked if Moore could be part of the Spurs group rhis season, the manager said: "We have to see.
"We have to analyse the last part of the transfer market, because we try to bring wingers, and then we speak with him, with his agent, with the club, to find the best solution for everyone."
It is an update from De Zerbi which could trigger an Ibrox alert as Rangers also seek a winger for the coming season, which kicks off next weekend.
Moore won Young Player of the Year last season and knows what it takes to play for the Light Blues.
Should they wish for another loan stint, Spurs may wish to do business again.