Spurs clinched their survival in England's top-flight almost two weeks ago with a 1-0 victory over Everton, and since then, they've been focused on getting some early business done.
Tottenham have already agreed to sign Marcos Senesi and Andy Robertson on free transfers from Bournemouth and Liverpool, respectively, while Jan Paul van Hecke is another defender catching their eye.
De Zerbi was a huge fan of the Dutchman during his time at Brighton, and according to David Ornstein on Thursday, an opening bid for the 25-year-old has been rejected.
Van Hecke, who has one year left on his contract at the AMEX, would be open to joining the Lilywhites, and another Premier League star could follow him.
Sky Sports revealed that Spurs are "considering" an offer for Manchester City winger Savinho, less than a year after their advances for the Brazilian were snubbed by Pep Guardiola.
Savinho only started two of City's final 19 Premier League games, and with Enzo Maresca's arrival pending, the 22-year-old's exit could be sanctioned.
Guardiola lauded Savinho as "unstoppable" after scoring in the Carabao Cup against Newcastle United in March. However, his talent would arguably be even more appreciated in north London.