Spurs are turning to Savinho with Arsenal set to win the battle for Crystal Palace attacking midfielder Ebere Eze.
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The Sun says Spurs hope to convince City to sell with a club record bid of £69m.
A previous offer of £50m by Spurs was rejected by City.
Savinho's agent is now in England and holding talks with both clubs in an attempt to thrash out the Brazil international's future.
For his part, Savinho has concerns about where he fits in City's plans following the arrivals of Omar Marmoush, Tijjani Reijnders and Rayan Cherki.