Spurs are hopeful of completing the deal for the 25-year-old before Thursday’s 17:00 BST transfer deadline.
Manchester United ended their talks with the Argentine because of his wage demands.
The move comes after Spurs abandoned their interest in Sporting Lisbon midfielder Bruno Fernandes, 24, because of the Portuguese club’s asking price.
Dybala joined Juventus from Palermo in 2015 for £23m and scored 10 goals for the Italian champions last season.
He also scored in a friendly against Novara in Turin on Wednesday.
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Mauricio Pochettino’s side have also agreed to sign Fulham’s England Under-21 left-back Ryan Sessegnon for £25m with Spurs midfielder Josh Onomah moving the other way.
In addition, Spurs’ proposed signing of Real Betis and Argentina midfielder Giovani lo Celso, 23, is likely to be on loan with an obligation to buy.
During pre-season, Pochettino said he was “not in charge” of signings and should change his title from manager to coach.
“I know nothing about the situation of my players,” said Pochettino.
“It’s true that ‘manager’ is a word that means different things than head coach. Maybe I was always manager from the first day I arrived here – and maybe it describes my job better.”