By Michelle Caruso-Cabrera, CNBC

Call it hedge-fund shuttle diplomacy. Flights from New York and London to Athens are seeing a lot of hedge fund managers. 

  The investors are meeting with the economic team of leftist leader Alexis Tsipras who, if the polls are right, could become the next prime minister of Greece after elections this month.

The political leader has been consistent with rhetoric that the European Union and International Monetary Fund need to change the terms of a their 2012 bailout of Greece, and it's gotten some market watchers concerned that the Mediterranean country will end up leaving the euro zone—either of its own accord or by being pushed out.  

  As a result, Greece's 3-year bond yield has shot as high as 15 percent this week, at a time when yields all over the world are falling. And four of seven hedge fund managers who spoke with CNBC say they're betting on that debt now.

But some of those managers have come away from meetings with the Tsipras economic team using the word "pragmatic" and concluding that a Greek exit from the common currency is unlikely.

What may be more likely is that Tsipras will push the European Union to forgive what are called "official sector loans." Those are loans Greece has obtained through bailouts by other governments. The hope is that Tsipras may not push for loan forgiveness from the private sector—the types of bonds held by hedge funds.  

  Greece's outstanding debt is 321 billion euros ($380.5 billion). But only a small percentage, roughly 36 billion euros ($42.7 billion), is made of privately held government bonds that trade on the open market. The vast majority of Greece's debt is owed to what's called the official sector.

Lawmakers in German Chancellor Angela Merkel's coalition said that they're open to the idea of extending the maturities on the Greek debt, according to a report Wednesday from Bloomberg, and they may also be willing to consider lowering the interest payment if Greece sticks to some kind of reform program.  

  That possibility has led some hedge fund managers to believe there is room for a deal. However, debt yields are still extremely high—making it clear that theirs is still a minority view.

That's also what makes the debt attractive—and why some hedge funds privately admit they are buying it.