Regarded as one of the most promising strikers in Argentinian football, the 19-year-old has become a mainstay of the Rosario first team and has already made 62 appearances for the club.
Veliz has come up with 19 goals and two assists for his boyhood club in that time, including 11 goals from 23 matches in the recently-ended Liga Profesional campaign.
Only five players scored more goals than Veliz in the 2023 Argentine Primera Division, and he also made waves for the Argentina Under-20 team at the recent World Cup.
Under the tutelage of Javier Mascherano, Veliz scored in three successive group matches against Uzbekistan, Guatemala and New Zealand before Argentina suffered a shock last-16 exit to Nigeria.
The 6ft 1in striker is still contracted to Rosario for another two-and-a-half years, but according to Fabrizio Romano, Veliz is now pining for a transfer to Tottenham Hotspur.
Romano claims that Veliz has accepted a long-term contract proposal from the Lilywhites, who are now locked in negotiations with Rosario Central over a fee.
Should Spurs find an agreement with Rosario, the Argentine club would apparently want to keep Veliz on loan for another six months before the striker joins Tottenham in early 2024.
A separate report from the Evening Standard claims that Spurs have been quoted £12m to sign the Argentina Under-20 international, which the Lilywhites will seemingly have no problem forking out.
Veliz could potentially arrive in North London as a successor to Harry Kane, whose future remains one of the major talking points of the transfer window amid Bayern Munich's relentless pursuit of his signature.
A Bayern delegation including sporting director Jan-Christian Dreesen and technical director Marco Neppe reportedly met with Daniel Levy in London on Monday, during which the Tottenham chief turned down a fresh bid worth £85m.
While Kane remains open to an Allianz Arena switch, the England captain supposedly expects to remain at Tottenham if no agreement is found before Spurs' Premier League opener with Brentford on August 13.
The Lilywhites have brought in a trio of new faces in Guglielmo Vicario, Manor Solomon and James Maddison this summer, and new head coach Ange Postecoglou is also working to beef up his side's defence.
Tottenham are now understood to be close to an agreement for Wolfsburg defender Micky van de Ven, while Blackburn Rovers' Ashley Phillips is set to join in a £2m deal when his release clause kicks in on Friday.
Postecoglou's side welcome Shakhtar Donetsk to North London for a charity friendly on Sunday, two days before taking on Barcelona in the Joan Gamper Trophy.