National news agency DPA quoted "government sources" as saying that the ministry's number two, Stephane Beemelmans, had informed parliament's defence committee about the decision late yesterday.
The reduction had already been decided in late 2011 by the then defence minister Thomas de Maziere, the report said.
Out of the total order, more than 100 jets worth around USD 19.2 billion have already been delivered, it added.
The defence ministry and manufacturer Eurofighter Jagdflugzeug GmbH did not comment on the report.
Defence Committee chairman Hans-Peter Bartels meanwhile said Germany should further cut its Eurofighter fleet, according to business daily Handelsblatt.
"We should reduce the Euro Fighter fleet to 108 machines, that's enough," he said.
The Eurofighter consortium, Europe's largest defence programme, is in fierce competition with other fighter-jet makers such as Lockheed Martin, Boeing and Dassault Aviation.
Industry players and analysts voiced little surprise over the reduced German order of Eurofighters, a joint project of the Airbus Group, BAE Systems and Italian defence group Finmeccanica.
Edward Hunt, senior consultant at IHS Defence, said that "the decision not to acquire the 37 aircraft is not unexpected" and "has been on the cards for a while".
"Germany has been focussing on other air force and defence requirements over the last 10 years or so and does not appear to consider its fast jet fleet as much of a priority," he said.
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