The troika comprises envoys from the US, the EU and Russia.
The ongoing diplomatic efforts are a final push for compromise on the fate of the UN-run Serb province, whose two million ethnic Albanians constitute a demographic majority.
The troika envoys began their mission in July after a UN resolution calling for Kosovo's statehood was blocked by Russia, acting in support of its ally Serbia, after 13 months of fruitless Serb-Albanian talks.
The three envoys met leaders of the ethnic Albanian community in Pristina on Sunday after arriving from Belgrade, the Serbian capital, where Serb leaders repeated their opposition to independence.
Ischinger said: "We are urging both sides to think outside the box.
"If both sides repeat their classic positions, there is little hope for compromise or bridge-building."
He said an agreed solution presented to the UN Security Council would be in the best interests of all concerned.
Western policy on Kosovo previously ruled out partition, arguing it could spark regional conflict.
Any division would be likely to leave the northern slice, where about half of Kosovo's 100,000 Serbs live, as part of Serbia.
Despite the mediation efforts, Kosovo, is likely to declare independence unilaterally and seek recognition from major Western powers.
|Ceku is committed to independence [AP]|
Kosovo's leaders have called for independence from Serbia by the end of 2007 despite efforts to seek a compromise solution by international mediators from Russia, the US and EU.
Agim Ceku, Kosovo's prime minister, said: "I am working for the recognition of the independence of Kosovo, in its current borders ... this year."
The "troika" group is due to report back to Ban Ki-moon, the UN secretary-general, by December 10.