During the summer, Spurs paid in the region of £12m to secure the signature of the young Argentine frontman from Rosario Central.
Upon his arrival, it was anticipated that the 20-year-old would rarely be used in the first team as he acclimatised to the rigours of English football.
That is how it has proven with just 45 minutes of football being provided to Veliz across eight appearances in the Premier League.
On December 28, Veliz scored his first goal for Spurs in the 4-2 defeat at Brighton & Hove Albion, but he sustained an injury to his knee in the game with Bournemouth three days later.
As it stands, the Argentina Under-20 international is expected to return to action at the beginning of March, Spurs having to cope with his absence in the meantime.
However, with Son Heung-min due to return from the Asian Cup, Timo Werner having been signed from RB Leipzig and Spurs being eliminated from the FA Cup, further opportunities in the senior ranks this campaign could be rare.
According to the Daily Mail, Spurs are now weighing up whether they should allow the prospect to spend the rest of the season elsewhere.
Sevilla are said to have proposed a loan deal, believed to come with no options or obligations, for Veliz to make the temporary switch to Spain.
Current backup striker Rafa Mir has been targeted by the likes of Valencia - one of his former clubs - and Torino, and it appears likely that the versatile attacker will be allowed to go out on loan.
That would leave Sevilla requiring backup for Youssef En-Nesyri at a time when they have won just three of their 22 La Liga fixtures in 2023-24, leaving Los Nervionenses just one point above the relegation zone.