The 17-year-old has been linked with the likes of Borussia Dortmund, Bayern Munich and Chelsea in recent months.
The youngster can leave Wolfsburg for a tribunal fee at the end of this season and now looks set to join Leverkusen.
Leverkusen general manager Rudi Voller told Deutsche Presseagentur: “Julian Brandt is to sign with us. We just do not know if this will take place this winter or next summer. We will have to agree that with VfL Wolfsburg.
“We are a top club (as shown by) we are able to sign top players like Julian Brandt.”
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