The La Liga outfit approached Spurs late on Wednesday regarding the 20-year-old, who as expected to remain in England for the campaign as he continues to adapt to Premier League football. Veliz has recently been sidelined through injury but is expected to be fit to train over the next two weeks.
But after being given assurances that Veliz will have plenty of first-team opportunities, Spurs agreed to sanction a temporary move away for the highly rated Argentine. There is no option to buy in the agreement.
Veliz is yet to start for Spurs since a summer move from Argentine club Rosario Central in the summer and Dane Scarlett's return from a loan spell at Ipswich has potentially forced the Argentina youth international down the pecking order in Ange Postecoglou's squad.
Winger Bryan Gil is staying put despite attracting interest from Brighton in the final days of the window, while Swedish wonderkid Lucas Bergvall was deciding his future after Spurs and Barcelona agreed fees with Djurgardens for the teenager.
The midfielder visited Spurs' training ground on Monday but was in Barcelona later in the week. There is no rush on a deal being finalised as in any case he would not move until the summer.