"The odds we get some sort of a short-term deal are reasonably good. The medium and longer-term outlook to me is still quite troubling," Jain said in a CNBC "Squawk Box" interview ahead an important meeting between Greek Finance Minister Yanis Varoufakis and his euro zone counterparts in Brussels.
Varoufakis is expected to propose a four-pillar overhaul of his country's current bailout program.
Jain said, "We are poised at a pretty unfortunate juncture ... because Greece was definitely heading in the right direction."
The Greek austerity plan was working, he added, but acknowledged the political realities in Athens after the leftist government prevailed in last month's election.
"One has to respect democracy. But we now have a government which is moving in a different direction, which of course creates a level of tension between them and the troika, which has been funding them," Jain said, referring to the European Central Bank, International Monetary Fund, and European Commission.
"Nobody wants Greece to exit the euro zone," he said. "The sanctity of the euro zone is very important to players on all sides of the fence."
If Greece were to exit, Jain said, "the concern really would be a domestic concern for Greece itself because if you start getting deposit flight, which we've been seeing—as much as 10 billion euros out of the Greek banking system in the last month or there abouts—if that continues, the prospect of social unrest and so on does become quite real."
But he argued, "The broader contagion worries are lower in my head than they would have been a few years ago ... [when] we had other indebted countries in Europe and we didn't have the ECB programs that we have today."
"One can take comfort in the fact that real institutions have been built and real progress has been made in other parts of Europe in the past two or three years," the Deutsche Bank co-CEO said.