Spurs are determined to bring a new striker to the club before the end of this summer's transfer window, and Milik has been strongly linked with a move away from Naples in recent weeks.
Roma were thought to be at the head of the queue for the 26-year-old, but a proposed switch to Rome has allegedly broken down.
According to Calciomercato, Tottenham will meet Milik's agent in London today to discuss a move, and there is a hope that a deal could be reached for a fee in the region of £17.5m plus a potential £6m in bonuses.
The Poland international, whose current deal with Napoli is due to expire next summer, scored 14 times in 35 appearances at club level last term, including 11 goals in Serie A.
A previous report claimed that Spurs were prepared to offer Milik a five-year contract worth £90,000 a week.