Eder Militao and Antonio Rudiger are currently Real Madrid's starting centre-backs, with David Alaba out since last December with a serious knee injury, and it is still unclear when the Austrian will return.
Defensive midfielder Aurelien Tchouameni is also an option at the back, while Jesus Vallejo is another senior defender, but the 27-year-old has only made one La Liga appearance during the 2024-25 campaign.
Los Blancos continue to be heavily linked with Al-Nassr's Aymeric Laporte, with the former Manchester City centre-back said to be a leading target for the club ahead of next summer's transfer window.
However, according to AS, alternatives are being looked at, with Gomez among those who is liked by the club.
Real Madrid 'showing an interest in Gomez'
The report claims that River Plate and Boca Juniors are also interested in the 21-year-old, with Velez believed to be willing to let him leave for a fee in the region of €10m (£8m).
Gomez came through the youth system at Velez, progressing to the first team in 2022, and he has represented his current side on 98 occasions in all competitions, scoring three goals and registering one assist.
The defender is yet to win a senior cap for Argentina, but he represented their Under-20s side on 10 occasions.
Gomez is also capable of operating as a left-back, and his versatility will make him an even more attractive proposition for Real Madrid, especially as Fran Garcia is being linked with a move away from the club.
Will Real Madrid sign a centre-back in January?
Real Madrid head coach Carlo Ancelotti is believed to have asked the club to move for a new defender at the start of 2025.
However, it is now thought that the capital giants will wait until the end of the campaign, as there is hope that Alaba will be able to make his return to action before the end of the year.
Real Madrid will allegedly not sign a defender unless 'a very clear opportunity' crops up, with Tchouameni able to cover in that area of the field if either Militao or Rudiger pick up injury problems.
Laporte, 30, is still thought to be the club's leading centre-back target, although Real Madrid could ultimately decide to bring in a younger player, and at €10m (£8m), Gomez could be a real bargain considering his potential.