The Italian Treasury made no immediate comment.
Prime Minister Matteo Renzi has come under heavy pressure to compensate some 12,500 savers whose nest eggs vanished overnight when his government bailed out four banks under new EU rules that imposed losses on shareholders and some bondholders.
A government source told Reuters last week that the Treasury planned to ask private banks to help reimburse those hit by the rescue last November of Banca delle Marche, Banca Popolare dell'Etruria, Cassa di Risparmio di Ferrara and Cassa di Risparmio di Chieti.
A deposit protection fund paid for by all Italy's banks has been set up with 100 million euros ($113.65 million) but this would not be enough to cover all the losses and the government could ask for more from the banks, the source said.
Renzi has never said how much reimbursement he plans to offer, but has said on numerous occasions since last December that a proposal would be presented shortly.
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