Nato said it is considering Turkey’s request without delay.
Secretary-General Anders Fogh Rasmussen said: “Such a deployment would augment Turkey’s air defence capabilities to defend the population and territory of Turkey.
“It would contribute to the de-escalation of the crisis along Nato’s south-eastern border.”
Germany’s Foreign Minister Guido Westerwelle said he had told the country’s ambassador to Nato to approve Turkey’s request.
Only the United States, the Netherlands and Germany have the appropriate Patriot missile system available.
Speaking in the Bundestag lower house of parliament, Westerwelle said: “I’ve told the German ambassador to accept the request, of course if the necessary conditions are met.”
Rejecting the request would be a grave error, he said, with severe consequences for Nato.
Some German opposition politicians had voiced reluctance to send German patriot missiles to Turkey, fearing Germany could get drawn into the Syria conflict.
Westerwelle said he believed a Bundestag vote would be necessary on sending missiles from Germany.