The 19-year-old Argentina youth international has caught the eye for Rosario and his country at the recent Under-20 World Cup and, according to reports in Argentina, would cost Spurs around £12million.
Veliz, an imposing figure at over six feett tall, has 11 goals in 23 league games for far this season.
A number of Premier League clubs, notably Brighton, have tapped into the South American market in recent seasons to much success, including the likes of Moises Caicedo and Julian Alvarez.
Spurs are also looking to offload players and are open to offers for Hugo Lloris, Pierre-Emile Hojbjerg, Tanguy Ndombele and Bryan Gil, among others, although Gil is expected to be sidelined for around two months following groin surgery which may limit him to a loan move.
The club’s summer business, which is dominated by the question of Harry Kane’s uncertain future, is being led by chairman Daniel Levy, Postecoglou and chief scout Leonardo Gabbanini, with Spurs still actively hunting for a new director of football and no start date yet announced for incoming chief football officer, Scott Munn.