De Zerbi made the comment when asked about his club's recruitment plans ahead of a pre-season friendly against Chelsea in Australia, according to The Athletic.
Manchester City winger Savinho has been a long-standing Spurs target, with the two clubs maintaining regular contact over a potential deal, though City are understood to want a replacement lined up before sanctioning any sale. Tottenham have also registered their interest with the representatives of Liverpool's Cody Gakpo, though they have yet to make contact with the Merseyside club or open formal negotiations.
Liverpool have no intention of selling the Dutch international, but would weigh his value against other business done elsewhere this summer, including Elliot Anderson's move to Manchester City and Morgan Rogers' transfer to Chelsea. Liverpool are also keen to add to their attacking options rather than subtract from them, and are mindful that new manager Andoni Iraola has not yet had the chance to work with Gakpo.
Spurs have also expressed an interest in Eintracht Frankfurt winger Jean-Mattéo Bahoya and held talks with the French winger's representatives before the window opened, though he has never been viewed as a primary target and there has been no club-to-club contact so far.
The 21-year-old, who is also drawing interest from Saudi Arabia, was Bundesliga's fastest player last season and ranks among Europe's most productive dribblers, according to figures cited by The Athletic. AC Milan forward Rafael Leao remains a name in the conversation too, with contact between the Italian club's recruitment staff and his representatives before the World Cup, though nothing has progressed since and he is not currently considered an active target by Tottenham.
Spurs have already spent heavily this summer, with fees totalling more than £230m on the likes of Sandro Tonali, Mateus Fernandes and Jan Paul van Hecke, and have been repeatedly linked with Savinho as their clearest attacking priority.
De Zerbi's determination to add further firepower comes with several forwards already sidelined: Dominic Solanke, James Maddison and Mohammed Kudus all had significant injury spells last season, while Wilson Odobert and Xavi Simons remain out with long-term knee problems.