Let's make sure we understand what's at stake here: If this is true then the ECB and Italy had better put a stop to it right now. Like before Europe opens. This means that if the "rumor" is false the banking authorities need to get on the air right now and refute it with hard facts, not platitudes and denials.
If there is a deposit run on Italian banks that is not immediately stemmed it will result in a severe and probably intractable liquidity crisis that will (1) shut down lending in Italy and (2) result in one or more of the involved banks blowing up as it goes under regulatory capital minimums - or worse, simply runs out of liquid funds period.
The Euro zone has no meaningful way to deal with this. Forbidding transfers out will simply make the panic worse in that it will confirm that the bank(s) involved can't cover withdrawals. Doing nothing is unacceptable as well. And if these institutions blow up, we're going to get a replay of Creditanstalt and all of its knock-on effects, right here, right now.
I do not normally reprint rumors at all, as they tend to be very destructive, but this is a special case because the risks, if the rumor is correct, are exceedingly high. I'm sure you thought the 500 point loss on the DOW today was horrifying, never mind the 60 handles on the S&P 500 that came off and the 105 (!) on the Nadaq 100.
Here's a hint: Those are small numbers if a major bank in Italy blows up in an uncontained fashion.
I have no idea if this is real or not. But we've seen, according to Bloomberg, $2 trillion come off stock market valuations in the last ten days.