Debt conundrum to keep Greek banks in months-long freeze

* Cash controls set to stay until fresh capital arrives

* Debate centres on losses for creditors, Athens' control

* Athens pushes for quick cash injection but talks could drag on

By John O'Donnell, Lefteris Papadimas and Francesco Canepa

FRANKFURT/ ATHENS, July 26 (Reuters) - Greek banks are set to keep broad cash controls in place for months, until fresh money arrives from Europe and with it a sweeping restructuring, officials believe.

Rehabilitating the country's banks poses a difficult question. Should the euro zone take a stake in the lenders, first requiring bondholders and even big depositors to shoulder a loss, or should the bill for fixing the banks instead be added to Greece's debt mountain?

Answering this could hold up agreement on a third bailout deal for Greece that negotiators want to conclude within weeks.

The longer it takes, the more critical the banks' condition becomes as a 420 euro ($460) weekly limit on cash withdrawals chokes the economy and borrowers' ability to repay loans.

"The banks are in deep freeze but the economy is getting weaker," said one official, pointing to a steady rise in loans that are not being repaid.

This cash 'freeze' is unlikely to thaw soon, although capital controls may be slightly softened, such as the loosening on Friday of restrictions on foreign transfers by businesses.

"Ultimately, you can only lift the capital controls when the banks are sufficiently capitalised," said Jens Weidmann, the head of Germany's Bundesbank, which pushed the ECB to pare back bank funding, leading to their three-week closure.

The debate is interlinked with a wrangle over reforms, about Greek sovereignty in the face of European controls and whether the country can recover with ever rising debts that have topped 300 billion euros, far bigger than its economy.

Were another 25 billion euros to be piled on top - the amount foreseen for the recapitalisation of Greek lenders - it would add to debts that the International Monetary Fund has argued are excessive.

BERLIN CALLING

Greek officials, alarmed by a downward spiral in the economy, want an urgent release of funds for their banks.

Four big banks dominate Greece. Of those, National Bank of Greece, Eurobank and Piraeus fell short in an ECB health check last year, when their restructuring plans were not taken into account. The situation is now dramatically worse.

"We want, if possible, an initial amount to be ready for the first needs of the banks," said one official at the Greek finance ministry, who spoke on condition of anonymity. "That should be about 10 billion euros."