German policy was geared towards keeping Turkey neutral (preferably 'friendly neutral'); the Turkish leaders' determination to remain neutral was evident to the Nazi ambassador to Turkey from 1939 to 1944, Franz von Papen. Thus, attempts to sway the Turks were aimed more at gaining favours rather than an outright declaration of war on the allies. On two occasions, Germany offered Turkey territorial inducements but neither offer was accepted as these would have jeopardized Turkish neutrality and / or had other adverse effects.
Throughout the war, Turkish armed forces were deployed according to their strengths (i.e. defensively) and overwhelmingly in the west. A move against Baku would have gone against their desire for closer relations with Soviets (though the Molotov–Ribbentrop Pact temporarily made this impossible) and would have threatened their existing access to oil through British-controlled Iraq.
The Turkish policy of neutrality was driven primarily by her fear of joining the wrong side (i.e. the losing side, as had happened during WWI) and the perilous state of both her economy and her poorly equipped (though sizeable) army. Nonetheless, Turkey had (from the German perspective) worryingly close ties with Britain; the UK supplied arms to Turkey (as did the US from 1941) and bought up supplies of chrome years ahead to lessen Turkish supplies to Germany of this key raw material.
However, the fall of France followed by Axis control over Greece, Yugoslavia and Bulgaria (among others) did force Turkey to adopt a more 'balanced' neutrality between 1940 and 1943. Turkey did receive a guarantee from Hitler in March 1941 that its borders would not be violated, a guarantee which, judging by the the expansion of the Turkish army and its massive deployment on their western border, they unsurprisingly weren't very convinced by. One result of these early Germany military successes was the German–Turkish Treaty of Friendship of June 1941. This was less than the Germans had hoped for as von Papen had
attempted to get permission for German troops to pass through Turkey
to attack the British and French in Iraq, Syria, and Iran, promising
in return territories in Thrace and a guarantee of Turkish security.
Turkey, however, realized that agreement to such terms would mean
essentially a declaration of war on the Allies; thus it ultimately
agreed only to a treaty of nonaggression with Germany...
Source: Stanford J. Shaw & Ezel Kurel Shaw, 'History of the Ottoman Empire and Modern Turkey: Volume II: Reform, Revolution, and Republic: The Rise of Modern Turkey, 1808-1975'
Then, in 1942, again at the instigation of von Papen,
Germany furthered its propaganda war in Turkey by promising German
assistance to the right-wing in supporting the Pan-Turkic movement,
especially in the reversion to Turkey of Moslem-speaking areas of the
Soviet Caucasus. While many Turks would have appreciated adding these
Soviet lands to their own territory, not even the Pan-Turkists,
however, wanted to give Stalin or his armies the slightest pretext to
slaughter the Turko-Mongol minorities then still firmly under Soviet
Source: Jerrold Michael Packard, 'The European Neutrals in World War II' (MA thesis, 1989)
Ultimately, though, the Germans were not prepared to push Turkey too hard. According to intercepted messages sent in July 1942 between the Japanese embassy in Ankara and the Japanese foreign ministry,
von Papen described Germany as avoiding any interference in Turkish
affairs but rather patiently waiting for Turkey to decide when it
would abandon its neutrality. Von Papen told the Japanese Ambassador,
"So far I have taken a mild attitude and tried to use what I might
call ‘gentle persuasion' on them. Now, even though the situation is
rapidly changing [after Axis military successes in Egypt against the
Allies], I intend to continue acting the same way."
The Japanese ambassador speculated that the Turks had secretly given Germany some assurance of future support, but there appears to be no evidence for this. In fact, the Japanese had already been told by a Turkish minister that "Turkey was determined to maintain her neutrality to the end."
From a military point of view, neutrality was also the best policy. The Turkish army was considered an effective defensive force by contemporary foreign observers and its military installations on its borders were of a defensive nature. In the mid 1930s, the army was between 130,000 and 180,000 strong. By May 1939, this had risen to around 300,000 and less than a year later, as Nazi power in the region grew, it had been boosted to 1,300,000. However, a serious lack of arms meant that most of these extra personnel were engaged in non-military activities such as road-building, porterage and other types of labour. Further, Turkey's armoured divisions were limited and poor quality, as was its air force. Thus, the country was ill-equipped for offensive operations such as an invasion of the Caucasus. Finally, joining the Axis for an attack on Baku would have exposed Turkey's dependence on Britain as the latter controlled key parts of the Middle East. Turkey's oil came from Iraq and
the rail line through Syria and Iraq represented, in the context of
the times, its last secure link with the outside world...
Source: Brock Millman, 'Turkish Foreign and Strategic Policy 1934-42'. In 'Middle Eastern Studies Vol. 31, No. 3' (Jul., 1995).
Jeopardizing this essential link without already having a guaranteed alternative oil supply in place would not have made sense.
There were other inducements offered, such as more up-to-date arms for the Turkish military and agreeing to buy surplus produce at highly-inflated prices, but these were aimed at obtaining high grade chrome rather than getting Turkey to join the Axis. Further, as already noted, Britain and the US were already supplying Turkey and buying her chrome at highly-inflated prices.
Selim Deringil, 'Turkish Foreign Policy During the Second World War: An 'Active' Neutrality' (2004)
Selim Deringil, 'The Preservation of Turkey's Neutrality during the Second World War: 1940'. In 'Middle Eastern Studies, Vol. 18, No. 1' (Jan., 1982)