Germany received the request several days in advance, the Allgemeine Zeitung confirmed. A spokesman for the defense minister declined to provide further details or say whether Germany would supply the missiles to Ukraine.
Britain was the first country to supply Ukraine with the missiles in early May, Reuters reported.
The United States has so far declined to supply Ukraine with the 297-km range Army Tactical Missile System (ATACMS) missiles amid concerns that Ukraine could use them to strike inside Russia's internationally recognized borders.
For months, Ukraine has held bilateral meetings with the heads of state of various countries to seek their support for such weapons. So far, countries have provided Ukraine with shorter-range weapons.
Taurus is built by European missile maker MBDA and has similar features to the British Storm Shadow.
It can be used to hit high-value targets, troops or fuel dumps deep behind the front lines and has the capability to destroy hardened targets such as bunkers buried deep underground.