Leverkusen lost its main shirt sponsor this year after the energy company TelDaFax ended its two-year deal.
The club, which is in the Bundesliga, German's top division, is now running an ad in the FT that states "Come and play the Champions League with us!
"This is your opportunity to become the main sponsor for Bayer 04 Leverkusen."
It is unclear if the ad, which appeared this week, was placed by the football club or by a sport sales house on its behalf.
However, sponsorship experts agree that it is highly unusual to place an ad in a UK business paper.
Andy Sutherden, managing director sports marketing and sponsorship at Hill & Knowlton, said: "My sentiment is that it is an innovative way of spending the same sales budget to acquire a shirt sponsor."
Leverkusen, whose players include former German captain Michael Ballack, reached the European Champions League final in 2002.
According to the Audit Bureau of Circulation (ABCs), the title's circulation was 362,685 in May, which included around 20,000 bulk copies – those copies that are distributed for a nominal fee to selected hotels and airlines, but which are free to the reader.