Jurgen Klopp’s side reached the Wembley showpiece courtesy of a 4-3 aggregate win over Real Madrid and will meet their Bundesliga rivals there after they easily dispatched Barcelona over two legs in the semi-finals.
But, having received an allocation of just 24,000 tickets per team, Dortmund will be unable to satisfy even one 10th of the demand.
“We’ve followed how much sympathy people have towards us with great excitement,” marketing director Carsten Cramer told the club’s official website.
“More than 500,000 applications are a clear sign of Echte Liebe (true love, the club’s motto) which Borussia Dortmund fans feel towards the club and our authentic and successful team.”
Dortmund CEO Hans-Joachim Watzke also expressed regret over the situation, adding: “We’re sorry that we’re not nearly able to fulfil the wishes.
“Ten years ago, every club member would have had a chance to secure a ticket.”
The 2013 final, the second to be held at Wembley in three years, is scheduled for Saturday May 25.