Wirtz, 21, is widely regarded as one of the best young playmakers in world football, and he has been in excellent form for Leverkusen in the early stages of this season.
The Germany international has scored five times and registered one assist in six appearances, including a brace in Leverkusen's 4-0 win over Feyenoord in the Champions League on Thursday night.
Wirtz has a contract with Xabi Alonso's side until June 2027, but he is widely expected to be on the move next summer, with a number of the biggest clubs in world football said to be interested.
Manchester United, Manchester City and Bayern Munich are all thought to be admirers of the German, with the latter potentially viewing him as a replacement for Jamal Musiala, who is being linked with an exit.
Real Madrid 'the favourites' to sign Wirtz
However, according to Bild, Real Madrid are leading the race, with Los Blancos in pole position to sign him during next summer's transfer window.
The report claims that Leverkusen are likely to ask for around €150m (£126m) for the attacker considering his potential, and the length of time left on his contract.
There have been suggestions that Real Madrid want to appoint Leverkusen manager Alonso as their new head coach as soon as next summer, which would strengthen the Spanish outfit's position.
Indeed, Wirtz has a close relationship with Alonso and thrived under the Spaniard last season.
The attacker has managed 46 goals and 51 assists in 158 appearances for Leverkusen in all competitions, including 28 goals and 35 assists in 112 appearances.
Would Wirtz be a good signing for Real Madrid?
Wirtz again showed his class on his Champions League debut on Thursday, netting a brace against Feyenoord, while he was one of Germany's best performers at Euro 2024.
The attacker has already achieved a lot at the age of 21, but he also has a lot to work on, and the tools are there for him to become one of the best players in world football.
Real Madrid are said to be willing to pay a huge fee for Wirtz, and adding him to a squad which already includes the likes of Jude Bellingham, Vinicius Junior and Kylian Mbappe is a scary thought for rival teams.
Bellingham would be asked to play in an even deeper role if Wirtz arrived, but it is not impossible to imagine a switch being made to a front two during the 2025-26 campaign, with Mbappe and Vinicius operating through the middle, allowing Wirtz to potentially join Bellingham, Valverde and Aurelien Tchouameni in midfield.