The highly-rated 17-year-old is thought to have attracted the interest of Chelsea and a number of top other European clubs including Bayern Munich and Borussia Dortmund after impressing for Wolfsburg's youth ranks.
The Germany youth international winger is yet to make his Bundesliga bow, but is regarded as one of the best young talents in Europe.
Wolfsburg were keen to tie down Brandt to a new long-term deal, but the player has rejected their offer and looks set to leave on a free transfer when his contract expires next summer, even though Wolfsburg will be due a compensation fee for his education.
A Wofsburg spokesperson confirmed to Deutsche Presseagentur: "Julian Brandt has turned down the offer to sign a new contract with VfL Wolfsburg.
"As he is out of contract at the end of the campaign, Julian Brandt will therefore depart from VfL Wolfsburg."