I would like to expand onto this question, what were the axis powers plans for the middle east.
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I have not seen any concrete evidence to suggest Germany wished to invade Jerusalem, rather there were meetings and discussions to send German Jews to jerusalem, in an attempt to remove them from Europe and Palestine, which is important to note. Though the Germans weren't actively pursuing an occupation of the Middle East, they certainly didn't mind a de-stabilization of the region. There was a series of Iraqi coups in in the pre-war era against the British supported regency, and then another in 1941 staged by the Grand Mufti, Haj Amin El Husseini. He wanted to destabilize the Middle East and used WW2 as the catalyst to initiate a revolt since British troops were tied up fighting the Axis in Europe and North Africa.
At the Nuremburg trials, the official transcritps revealed that Adolf Eichmann held meetings with the Mufti when he visited Palestine in 1937 where they discussed removal of German Jews to Palestine in the event of an Arab take-over. He also sent several emissaries and travelled himself to Berlin in 1940.
The Mufti wrote in his memoirs:
"Our fundamental condition for cooperating with Germany was a free hand to eradicate every last Jew from Palestine and the Arab world. I asked Hitler for an explicit undertaking to allow us to solve the Jewish problem in a manner befitting our national and racial aspirations and according to the scientific methods innovated by Germany in the handling of its Jews. The answer I got was: 'The Jews are yours."
The Mufti was forced to flee Palestine in 1939 after the British made him a high-profile target and began his movement to revolt in Iraq, which was already largely anti-British. The Iraqi government funded the Mufti and he rapidly gained popular support. On April 1, 1941, the Mufti and his "Golden Square" (four pro-Axis staff officers: Salah al-din al Sabag, Fahmi Said, Mahmud Salman and Kemal Shabib) staged the coup, and appointed Rashid 'Ali al-Keilani head of the government, as the British supported regency were forced to flee. On April 3, a letter from the German Secretary of State Von Weizacker answered a request for military aid from Chief of staff Haddad "favorably."
It is reported that Hitler approved military aid to the Iraqi revolt in the sum of "some 15,000 rifles and about 800 machine guns. Arms were shipped from Saloniki and through Turkey and Syria. The shipments from Syria were sent as a consequence of the agreement between the Vichy leader Darlan and Hitler as to general collaboration between Vichy and Germany."
The Axis did provide military support in a very limited role. Despite difficulty in sending supplies, the Germans did manage to send 4 Bf110 twin engine fighters and 7 He111 bombers which arrived in Vichy Syria on 13-14 May 1941, and attacked the RAF airfield at Habbaniya immediately on arrival.
So to answer your question, no the Germans did not have any plans for occupying Jerusalem, but they did see opportunity to destabilize the region. The Italians, however, did want to conquer the Middle East. This is very important, as it falls under Mussolini's envisioned "glory of the Roman Empire," often called Mare Nostrum. During the revolt, Mussolini sent 12 Fiat CR.42 Falco's that actively engaged the RAF on numerous occasions. this is important because it was still early war, and had the Italians been successful in the Egyptian invasion, they certainly had their sights to move into the Middle East and recreate the Mare Nostrum of the Roman Empire. In fact, the Ciano Diaries reveal that the Italians had been funding the Mufti since 1936, around the origin of the Arab unrest. The Italains had a particular interest in the region, and though information is scarce, it does indicate that the Middle East was on the list of Italian imperial targets.
Sources:
Barrie, James G. Hitlers Gulf War, Pen & Sword Books Limited. London, 2010
Burgwyn, James H. Mussolini Warlord: Failed Dreams of Empire, 1940-1943, Enigma Publications.
http://www.mideastweb.org/iraqaxiscoup.htm
Official Nuremberg transcript detailing Eichmann and the Grand Mufti's relationship: http://www.nizkor.org/hweb/people/e/eichmann-adolf/transcripts/Sessions/Session-016-03.html
Also was the UK anticipating having to defend the area from Nazis?