The Brazil winger only moved to City a year ago from Girona and is regarded highly by manager Pep Guardiola.
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However, the Mirror says Spurs are convinced Savinho could become available after the arrival of Rayan Cherki from Lyon.
There is a belief City would be willing to sell Savinho with Cherki now seen as ahead of him in the midfield pecking order.
Tottenham are expected to make an attempt this week for Savinho with new manager Thomas Frank eager to see more signings come through the door.