The 20-year-old has only earned fleeting opportunities in the Spurs XI since joining from Rosario Central over the summer, scoring once in eight Premier League appearances.
Three days after opening his Spurs account against Brighton & Hove Albion in December, Veliz sustained a serious knee injury against Bournemouth, which is expected to sideline him until March.
Despite his lengthy layoff, Sevilla showed an interest in taking the Argentinian for the remainder of the season, and according to Sky Sports News, he has passed his medical with Los Palanganas.
The report adds that the examinations took longer than usual due to Veliz's ongoing issue, but the striker is now on the verge of making the switch to La Liga for the remainder of the season.
Veliz will arrive at Sevilla with the Europa League holders languishing dangerously close to the La Liga drop zone in 16th place in the table, just one point clear of the dotted line.
The 20-year-old's contract at the Tottenham Hotspur Stadium does not expire until the end of the 2028-29 season.