Emergency aid is being supplied to the firm, with Hong Kong's central bank providing an extra $500 million to the financial system.
Lines of depositors formed outside of BEA branches, as the financial crisis led to nervousness over the stability of the city's financial system.
The rumors also triggered an 11 per cent drop in the price of BEA shares yesterday - although the stock recovered four per cent by 3pm today.
Branches are also experiencing a lessening in the queues, Bloomberg reports.
Bank chairman David Li termed the rumors "groundless" and said that the bank had "no problem".
He also confirmed that he would buy shares in BEA as proof of his confidence.
The city's financial secretary, John Tsang, said that the speculation was "malicious" and "unfounded".
Mona Chung, fund manager at Daiwa Asset Management, told the news agency that the reaction to the speculation "seems a bit exaggerated".
She added: "This is probably a bigger problem in the US than for local banks.''