The Belgian striker has emerged as a top target for a number of Premier League clubs after establishing himself in his homeland, and looks set to be the subject of much interest later this year.
But despite the 20-year-old having already admitted that he wants to join Arsenal, Spurs are planning their own £10m move.
Tim Sherwood is already believed to be lining up targets even though his future at White Hart Lane is unclear, and he sees Batshuayi as a good option.
With Roberto Soldado having misfired through his debut season in England and Emmanuel Adebayor having a reputation for a lack of consistency, a new forward is seen as a priority.
Tottenham are confident that they can persuade Batshuayi to turn his back on Arsenal and sign for them, and are hopeful that they can seal the deal before the World Cup starts.
Everton have also been linked with the man who has netted 18 goals in his last 29 matches.