The manager told reporters in Sydney the squad rebuild is only "60 percent" complete, with one more significant attacking addition still to come.
"The transfer market is not finished for sure, but we have completed 60% of our project. Now we have another 'bomba'," De Zerbi said.
Pressed on whether the mystery signing would be a winger or a striker, he replied: "Attackers. I don't love working with plan A, plan B, plan C. It is plan A, full stop, because all players are not the same. We have to increase the number of goals."
Manchester City winger Savinho is in advanced talks over a move to north London, though De Zerbi indicated the "bomba" may refer to a different, unnamed target altogether.
The Italian also addressed the futures of several unsettled players, starting with Djed Spence, who has been linked with Inter Milan and Everton despite signing a long-term deal last year.
"I repeat what I said to Djed, and to Lucas [Bergvall]," De Zerbi said. "I would like you to stay if you want to stay. If you don't want to stay, if you want to leave, then you have to leave."
Spence started 23 of his 30 Premier League appearances last season as Spurs finished 17th for a second straight year, but faces increased competition after the signing of Jan Paul van Hecke and with Spain's World Cup winner Pedro Porro entrenched in his preferred right-back role; Porro started 32 of Spurs' 38 league games last season and signed a new contract this year. "The best in the world," De Zerbi said of Porro's role.
Captain Cristian Romero is among those expected to leave, following criticism of his decision to fly back to Argentina while injured ahead of Spurs' final match of last season, before he ultimately returned for the game.
De Zerbi defended the defender's conduct while confirming an understanding had been in place since his arrival that players unhappy at the club could go.
"At the beginning of my time in April I had, I don't know, one million individual meetings. And the players told me if they are [staying] here or not," he said. "I said: 'Yes, help me to stay up, and then I help you to leave. If you don't help me to stay up, you stay underwater with me.'"
Goalkeeper Guglielmo Vicario is also expected to depart after losing his place to Antonin Kinsky.
Tottenham's spending this summer has included club-record fees for Mateus Fernandes (£85m, from West Ham) and Sandro Tonali (£100m, from Newcastle), along with Jan Paul van Hecke's £52m move from Brighton and free transfers for Marcos Senesi, Andrew Robertson and Martin Dubravka.