The reported agreement could also include a further 10 million pounds in add-ons, although the transfer has not been officially confirmed by either club.
Tottenham tried to sign the Brazil international last year but were unable to complete a deal. They have now reportedly returned for the winger and appear to have made significant progress in negotiations.
Savinho made 24 Premier League appearances for Manchester City last season and would add pace and attacking quality to Tottenham's squad.
Spurs have already strengthened their midfield this summer with the arrivals of Mateus Fernandes and Sandro Tonali, and Savinho would represent another major addition under manager Roberto De Zerbi.
Tottenham are also reportedly still in talks with Manchester City over a possible move for Egypt forward Omar Marmoush.
The club are due to begin their Premier League campaign away to Brentford on Saturday, with Savinho's reported move yet to be officially confirmed.
Liverpool manager Andoni Iraola has confirmed the club will continue adding to their squad before the transfer window closes on September 1, admitting the current group remains short of depth.
Arsenal have completed a 51 million pounds deal to sign England defender Ezri Konsa from Aston Villa, strengthening Mikel Arteta's options in defence.
Hull City manager Sergej Jakirovic has welcomed the doubts surrounding his side as they prepare for their return to the Premier League.
Bruno Guimaraes is a doubt for Arsenal's Premier League opener against Coventry City on Friday after picking up a leg problem in Sunday's Community Shield victory over Manchester City.
