The agreement was reported to include a further £10 million in add-ons and comes a year after Spurs' unsuccessful attempt to sign the Brazil international.
Spurs and Manchester City did not immediately respond to requests for comment on the reported signing.
Savinho, who made 24 Premier League appearances for City last season, would be another major addition to the Spurs squad after the arrivals of midfielders Mateus Fernandes and Sandro Tonali.
British media also reported that Spurs remain in talks over a move for City's Egypt forward Omar Marmoush.
Tottenham travel to Brentford for their opening game of the season on Saturday - follow it with Flashscore.
