The report posted on the website of the Handelsblatt newspaper and to be published in the Monday edition of the daily said the German regulator, Bafin, was about to grant the license to the Kuveyt Turk Bank AG.
The bank operates under guidelines that conform with Sharia law, meaning that it does not get involved in speculative ventures or investments, or those that do not comply with the teachings of the Koran.
This also means that it cannot charge interest on loans, but it may purchase assets and resell them for a profit.
The Handelsblatt quoted the bank's managing director Kemal Ozan, who said Kuveyt Turk hoped to tap into a wealth of potential customers in Germany, particularly among the four million Muslims who reside in the country.
"Our market research has shown that 21 percent of Muslims in this country would see an Islamic bank as their natural household bank," Ozan said.
Kuveyt Turk Bank already has a branch that is not fully functional in the southwestern German city of Mannheim.
Bafin's approval would allow it and future branches to operate as fully functional banks. Kuveyt Turk is reported to already have plans to open branches in Frankfurt, Berlin and Cologne.
pfd/msh (dpa, AFP)