Any deployment of Nato forces needs the approval of the alliance's governing body, the North Atlantic Council. But this is seen as a formality since Nato has already said it has plans in place to protect Turkey from a spillover of Syria's civil war.
"Allies will discuss this without delay," said Nato Secretary-General Anders Fogh Rasmussen.
He said the deployment would augment alliance member Turkey's air defence capabilities and "would contribute to the de-escalation of the crisis along Nato's south-eastern border."
Mr Fogh Rasmussen said the deployment of the US-built Patriots would not mean imposing a no-fly zone over Syrian territory, a key demand of Syrian opposition groups. Nato has installed anti-aircraft batteries in Turkey twice before, during the 1991 and 2003 Iraq wars.
They were never used and were removed a few months later.
Turkey's government said "in face of the threats and risks posed to our national security by the ongoing crisis in Syria ... it has been decided to formally request from Nato that our national air defence be reinforced with the support of allied air defence elements."
German Foreign Minister Guido Westerwelle said he had told the German ambassador to Turkey "to receive positively such a request."
He said "it would be a serious mistake if we were to refuse defensive support to a Nato member country in a moment when this member country feels that it is exposed to attacks from outside."