Los Blancos view the Valencia defender as the ideal replacement for Marcelo, who is expected to leave the capital club at the end of the season.
The Brazilian has been one of Real Madrid's key players for well over a decade but has been largely inconsistent over the last couple of years.
According to Spanish media outlet Fichajes, Real Madrid have joined the race to sign Valencia's Jose Luis Gaya. Zinedine Zidane's men will face heavy competition from Atletico Madrid and Barcelona for the services of the defender.
Los Blancos have the option of buying Sergio Reguillon back from Tottenham Hotspur for €40 million but reportedly prefer a move for the more experienced Jose Luis Gaya.
Jose Luis Gaya spent his youth career with Valencia before breaking into the club's first team in 2012.
The 25-year-old has become a key member of Valencia's squad and is currently the team captain. His consistent performances even earned him a call up to the Spanish national team in 2018.
The defender has been heavily courted by a number of La Liga's top clubs in recent seasons. Barcelona were interested in signing him last season but were unwilling to match Valencia's €40 million price tag.
Valencia likely to demand €50 million for Real Madrid target Jose Luis Gaya
Valencia are likely to demand a fee in the region of €50 million for Jose Luis Gaya. The Spanish side are willing to listen to offers for the defender as they look to raise funds and balance their books.
Real Madrid themselves are suffering financially and will look to negotiate a cheaper fee for the Spaniard.
Los Blancos are likely to spend big money on either Erling Haaland or Kylian Mbappe this summer, which is likely to deplete their capital reserves.