Spurs revived their interest in the Brazilian earlier this summer, having previously explored a move for him last year before City opted against a sale.
The pursuit has since been reactivated, with talks progressing steadily in recent weeks as the two clubs move closer to an agreement on structure and add-ons.
Savinho, 22, missed out on Brazil's World Cup squad after a mixed campaign at the Etihad, where limited game time under Pep Guardiola restricted him to appearances in cup competitions and rotation duty in the league.
He finished the season with 36 appearances in all competitions and four goals, a modest return for a player once considered one of City's most exciting attacking talents.
The Brazilian arrived at City from sister club Troyes before shining on loan at Girona, where he helped the Spanish side qualify for the Champions League, but has struggled to force his way into a settled starting role in Manchester since.
The Brazilian has previously been open to a move to north London, having agreed personal terms with Spurs during an earlier round of talks before City blocked a switch.
Tottenham's rebuild has continued at pace this summer, with the arrivals of Marcos Senesi and Andrew Robertson on free transfers already bolstering the defence, and a new wide attacking option would add further depth to a squad reshaped since avoiding relegation on the final day of last season.
For Manchester City, sanctioning Savinho's departure would free up space in an increasingly crowded forward line, with Guardiola having already signalled his willingness to trim a squad he considers too large following a busy summer of incomings at the Etihad.
Newcastle have also been credited with monitoring the winger's situation, though Tottenham remain the club best placed to complete a deal given the advanced state of talks.