It represents a first move that underlines the ambition of a club that only avoided relegation on the final day of last season and is now overhauling its entire squad.
Manchester City's valuation of Savinho stands at approximately £50m. The Brazilian had resisted Tottenham's approach last summer, preferring to remain at the Etihad Stadium and compete for a place under Pep Guardiola.
City, however, are rebuilding under incoming head coach Enzo Maresca and have become open to a sale after a season in which Savinho made 35 appearances but scored only four goals and contributed two assists, also missing time through a thigh problem.
The Savinho pursuit adds further momentum to a summer that has already seen Spurs confirm the free transfer of Liverpool left-back Andy Robertson, whose arrival brought a warm public endorsement from De Zerbi.
"Andy is someone I've admired for a number of years and he will bring outstanding technical qualities, experience, leadership and mentality to our team. He is a proven winner at the highest level over a long period and is someone who can be a big player for us, both on and off the pitch."
Tottenham have also agreed a deal in principle for Bournemouth Argentina centre-back Marcos Senesi and had an opening bid rejected for Brighton & Hove Albion's Jan Paul van Hecke, who is valued at approximately £70m, with talks ongoing.
Defensive exits are also expected — Cristian Romero is considered a likely departure, and there is strong interest in forward Mathys Tel.