Is your cash stuck in a Cypriot bank? Someone might be willing to take it off your hands.

Distressed-debt investors and brokers are circling Cyprus, the Mediterranean island that last month plunged its two main banks into an emergency restructuring and blocked thousands of depositors from touching all their money.

The idea: investors buy frozen bank deposits, at a discount. Depositors who need access to their money get a payoff immediately, instead of waiting months or years for the bank restructuring to be completed. Investors get a shot at a big payoff down the line.

The efforts are in their infancy; potential buyers are still sounding out lawyers on whether it’s even possible to buy the deposits. But if it is, there could be a developing secondary market in Cypriot bank deposits. Cyprus has imposed stiff capital controls that prevent anyone from transferring much money off the island. A trade in frozen deposits, then, is not far from a parallel market in “Cypriot euros.”

But, dear depositors, the price is steep: Angelos Paphitis, a lawyer in Limassol, Cyprus, said a distressed-debt fund (he declined to identify it, other than to specify it operates in the U.S. and Dubai) contacted him to work out the legal particulars, and was looking to offer 20% of face value for deposits in Bank of Cyprus PCL. He deemed it “nonsense.”

A small, London-based firm, Exito Capital, is trying to match buyers and depositors, and it says it has interest from both. Exito’s Ben Rosenberger and Michele Del Bo are former Lehman Brothers distressed-debt traders. They’ve traded Icelandic bank claims and claims on the bankrupt Lehman. Éxito itself hasn’t raised committed funds for Cyprus bank deposits.

Cyprus, they say, is an enticing case for both investors with a stomach for risk and depositors unlucky enough to be stuck. “It’s not the role of a corporate who had a deposit in Cyprus to stay in a distressed investment for five years,” says Mr. Del Bo. Initial estimates put the volume of affected deposits in the two banks at around €11 billion.

Cyprus passed emergency legislation in late March to restructure Bank of Cyprus and Cyprus Popular Bank PCL. Cyprus Popular, also known as Laiki, will be liquidated. Deposits of €100,000 ($136,700) or less will be transferred to Bank of Cyprus, and larger amounts will eventually be turned into claims against Laiki’s assets. It isn’t clear what those depositors will get, or when.

For depositors at Bank of Cyprus, the situation is more complicated. Deposits of €100,000 or less won’t be touched—though withdrawal and transfers restrictions apply. Depositors of larger amounts will see part of their depositors exchanged for shares in Bank of Cyprus, and the rest eventually returned—though it’s not clear how much and when.

Mr. Rosenberger says much of the interest from buyers is in Bank of Cyprus deposits, though he admits the waters are far from clear.

A chief problem is how to move deposits effectively from seller to buyer. Because the deposits are frozen, and the Cyprus central bank has imposed transfer restrictions, it’s not a simple matter.

One possibility is a side agreement that obliges the depositor to transfer proceeds to the investor whenever the deposits are freed up. That’s not wholly satisfactory, since there’s a risk the depositor could back out of the agreement. Mr. Paphitis, the lawyer, says the frozen deposits “cannot be assigned” from one party to another, and that a side agreement wouldn’t bind the bank that holds the deposits. “It is questionable,” he says.

Mr. Rosenberger thinks a solution will become clearer as Cyprus lays out the procedures for the banking wind-up. “We have to test the waters,” he says.

Charles Forelle