Berlin has already said it will provide Ukraine with 14 Leopard 2s from its military stocks, but manufacturers also want to send tanks they have in storage.
“I can confirm… that an export licence has been issued,” government spokesman Steffen Hebestreit told a regular press briefing when asked about Leopard 1s.
He declined to give further information, saying more details would likely emerge in the coming days and weeks.
First entering service in the 1960s, the Leopard 1 is the forerunner of the more advanced Leopard 2, which is widely used by armies across Europe.
German magazine Der Spiegel reported that it concerned 29 Leopard 1s, which were in storage at a military manufacturer.
The Süddeutsche Zeitung newspaper meanwhile reported that two manufacturers want to refurbish dozens of Leopard 1s to send them to Ukraine, although they have faced problems in procuring ammunition.
Last month, Berlin finally agreed to sending the powerful German-made Leopards to Ukraine, following weeks of sustained pressure from Kyiv and its European allies.
Under German law, Berlin has to approve the export of the tanks, even in cases when other countries who bought them want to re-export them.
While scores of nations have pledged military hardware for Ukraine in recent weeks, Kyiv has been clamouring for the more sophisticated Leopards, seen as key to punching through enemy lines.