The La Liga champions are believed to be among the 20-year-old's admirers, having monitored his progress for some time.
A recent report claimed that Wirtz had been included on a three-man shortlist of potential transfer targets alongside Royal Antwerp's Arthur Vermeeren and Porto's Alan Varela.
According to Bild, via Mundo Deportivo, Barcelona are not the only big European club showing an interest, with Bayern keen to bring the Germany international to the Allianz Arena.
The report claims that Bayern want to create a formidable attacking duo with Wirtz and his compatriot Jamal Musiala.
The pair played together in Germany's attack for Saturday's 3-1 victory over the USA, and it is a dynamic that Bayern want to utilise at club level.
The Bavarians believe that Wirtz and Musiala, who are both aged 20, could be a key part of their side for many years to come.
Wirtz played down the speculation surrounding his future when asked about the possibility of playing alongside Musiala at Bayern.
"We're having a very good season with Leverkusen so far, it's fun at the club," The youngster told Bild. "That's why I'm only thinking about Leverkusen."
"I still have a pretty long contract. That's why I don't need to worry about my future at the moment."
Contrary to previous reports, Wirtz does not have a release clause in his contract, which runs until the summer of 2027.
With Leverkusen keen to keep hold of one of their most prized assets, it would reportedly take an offer in the region of €100m (£86.5m) for them to consider a sale.
While Barcelona are continuing to keep tabs on the player, they are currently unable to meet Leverkusen's valuation due to the club's ongoing financial issues.
Wirtz has started the 2023-24 season in positive form, scoring three goals and providing four assists in 10 competitive matches.
In total, the playmaker has scored 26 times and contributed 34 assists in 113 appearances across all competitions.