Poor credit quality of banks usually goes hand-in-hand with poor government finances as the two institutions are “joined at the hip”, Egan told CNBC Asia’s “Squawk Box” on Wednesday. That’s the case for most countries such as the U.S., the U.K., Switzerland and Ireland; Spain and Italy are no exceptions, he said.

“It makes little sense to separate the banks’ credit quality from the governments’ credit quality because quite often, they support each other and that’s certainly the case in Italy and Spain,” he said. “We think that Spain will be back at the table, asking for more than the 100 billion euros ($125 billion) that they just asked for, and we think that Italy will also come to the table within the next 6 months.”

On Tuesday, worries over Spain’s finances sent its government bond yields to their highest since the euro was launched in 1999. Italian bond yields also rose after Austria's finance minister was reported as saying thatItaly may need a rescue because of its high borrowing costs.

A prompt denial by Italian Prime Minister Mario Monti that the nation needed a bailout from the EU did not stop investors from selling Italian equities and bonds.

The worries about Spain’s and Italy’s finances could spread to the rest of Europe, Egan said. Even Germany, seen as the nation with the soundest economy, may not be immune to the crisis.

Italy has Europe’s second-highest debt-to-GDP ratio, which stands at 120 percent, according to the International Monetary Fund.

“When you step back, you see that the combined economies for the EU have a fairly high debt-to-GDP,” Egan said. “There’s the assumption that Germany will be able to pull. That assumption may want to be re-examined.”

By CNBC's Jean Chua.