That is according to website Football Insider, who claim Tottenham chairman Daniel Levy has authorised a £16.5million bid to meet AZ's asking price.
And Spurs are reportedly confident of finalising the move over coming days in an attempt to beat fellow suitors Paris Saint-Germain to his signature.
The 21-year-old impressed with 32 goals in all competitions for the Dutch club last term and topped the Eredivisie scoring charts with 27 strikes.
Spurs manager Mauricio Pochettino has made no secret of his pursuit of a new striker this summer as he looks to add competition for Harry Kane next season.
Janssen, who will cost half the fee of Batshuayi, recently hit out at AZ - where he has three years remaining on his deal - after they turned down Spurs' initial offer.
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Vincent Janssen set to complete Tottenham move within the next two days
"I’ve made my choice clear to the club,” Janssen told Dutch publication AD last Thursday. "In my view, Tottenham Hotspur have made a big offer.
"There was an offer of about €18m (£15m). But AZ doesn’t even want to sit at the table. At the moment I’m still a bit disappointed. I would like to make the move."
The Sun claim Tottenham have also offered star striker Kane a new and improved five-year deal, worth £5m-a-season, after his 28 goals last season.
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