Shares in Westpac and St George are in a trading halt, with merger talks underway.
That would create the country's largest home lender.
St George has told the Australian stock exchange this morning that Westpac made the approach after close of business on Friday.
Channel Nine's Ross Greenwood has told 2GB's Alan Jones the combined entity would be worth around $58 billion.
"That would be rivallaling almost the value of the National Australia Bank, the country's largest [bank]," he said.
"They'd have 10 million customers, 1,200 branches, 2,700 automatic teller machines. Importantly, they say there would be no closures of branches and the other thing they're saying is that the St George brand would continue to run."
Westpac has approached St George Bank about a proposed merger.
Both banks asked for trading halts in their shares to allow talks to continue and for an announcement to be made, possibly within 24 hours.