Los Blancos have been tipped to sign a new midfielder amidst uncertainty over the long-term future of veteran Luka Modric, who is out of contract in June 2025.
Modric penned a short-term contract extension in the summer and was given the captain's armband following the departure of defender Nacho Fernandez.
The Croatian, who has spent the last 12 years at the Santiago Bernabeu, has already made 12 first-team appearances for Real Madrid this season, but at the ripe old age of 39, he is not getting any younger.
Recent reports have claimed that Real Madrid are one of several European clubs who are interested in signing Dinamo Zagreb midfielder Martin Baturina, who has been dubbed the 'next Modric'.
Real Madrid 'quietly' step up pursuit of in-demand Wirtz
However, Baturina is not the only 21-year-old on Real Madrid's radar, as Spanish news outlet Diario AS, via CaughtOffside, claim that Los Blancos are working quietly behind the scenes to recruit Leverkusen star Wirtz.
The Germany international is said to have been identified as Real Madrid's preferred long-term successor to Modric, although the Spanish giants would be required to fork out a whopping €150m (£125m) to secure his services.
Real Madrid CEO Jose Angel Sanchez and chief scout Juni Calafat are said to be leading the transfer pursuit of Wirtz, but they could face 'tough competition' from Premier League champions Manchester City in the race for his signature, according to Football365.
Arsenal and Liverpool are two more English giants who have been linked with Wirtz, with the former allegedly willing to meet Leverkusen's asking price in 2025.
Bayern Munich and Barcelona have also been credited with an interest in the versatile attacker, who is under contract at the BayArena until the summer of 2027.
Leverkusen's Wirtz a rising star in Europe
Wirtz is widely regarded as one of the brightest young talents in Europe and has developed into an integral first-team player at Leverkusen under head coach Xabi Alonso.
Despite rupturing his ACL in 2022, Wirtz has made a total of 162 senior appearances for Leverkusen across all competitions at the age of just 21, scoring 47 goals and registering 51 assists.
The creative midfielder was named 2023-24 Bundesliga Player of the Season after recording 11 goals and 12 assists in 32 league games to help Leverkusen with their first-ever German top-flight title and go the entire campaign unbeaten.
Wirtz, a 27-cap Germany international, has since scored six goals in 10 appearances at the start of this season, including four goals in six Bundesliga matches.