The 16-year-old is yet to make his first-team debut for Rayo but has trained with the club's senior side on a number of occasions during the 2019-20 campaign, having impressed at youth level.
A recent report claimed that Barca had beaten Madrid to the teenager's signature, although Luzzi is yet to sign a deal with the Spanish champions, meaning that his future is still up in the air.
Here, Sports Mole takes a closer look at the in-demand youngster.
Luzzi has been described by Marca as 'one of the most promising youngsters in the country'.
The teenager, as mentioned, is yet to represent Rayo's senior side but has been a regular during first-team training sessions in the second half of the 2019-20 campaign.
Born in Brazil but an Under-16 international for Spain, Luzzi has been the top scorer in each side that he has represented while coming through the ranks at his capital club.
The attacker turned 16 just last month, meaning that he has only just been able to discuss a professional deal, and various reports in Spain have suggested that Barca are already involved in negotiations over a contract.
Atletico Madrid have also been credited with an interest, but it appears that Real Madrid are Barca's main contenders when it comes to the talented forward.
Rayo are allegedly determined to keep hold of Luzzi at this stage of his development, but it will be difficult for the Segunda Division side to fight off the attentions of Spain's two biggest clubs.
Rayo could yet be able to hand the teenager La Liga football next season as they are currently battling to reach the playoffs in the second tier, occupying seventh position in the table.
Luzzi might have to wait to make the grade at Barca, though, with reports in Spain claiming that he would link up with their Juvenil A Under-19 side, run by Franc Artiga, should a move go through this summer.
The forward might not have made a first-team outing for Rayo, but he was named on the bench for their Copa del Rey fixtures against Barakaldo and Villarreal back in January, which is another indication of how highly he is rated.
It will certainly be fascinating to see what occurs in the coming weeks as Spain's top two seemingly lock horns for a player who is clearly regarded as one of the best young talents in the nation.
Luzzi's loyalties are with Rayo for the moment, though, and it would not be a surprise to see him involved in the first team between now and the end of the 2019-20 campaign.