The CCB has leased a section of the building from the district council for more than 10 years.
In November, CCB's board proposed a merger with Kernow Credit Union but the proposal was rejected by the members.
The Financial Services Authority said it has been in regular touch with CCB.
The CCB hopes to buy the property and create a visitor centre and cafe with space for exhibitions and training.
Silvia Fun, an analyst at CCB International, said the IPO moratorium has hurt Citic, the largest underwriter of share sales in China.
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The former board of Cornish Community Banking (CCB) had said it was "nearing insolvency" and suspended giving loans, causing difficulties for many members.
"This could all point to an acquisition by Bear, whose size could increase should CCB indeed provide several billion in additional capital, " Trone noted.
It is unclear just how a CCB investment in Bear Stearns would affect Bank of America's ownership in CCB or indirectly of Bear Stearns itself.
"In 80 major cities in China, CCB have almost 60% of all branches, making them the ideal partner to connect with our fans, " said United's Arnold.
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China Construction Bank (CCB) has its roots in development banking.
The diet continues at Bank of America, with the firm announcing Monday that it has agreed to sell the bulk of its remaining stake in China Construction Bank (CCB) to private investors.
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That figure is on top of a planned reduction of 3, 000 to 4, 000 workers in CCB at large, though in the broader segment expenses are expected to increase modestly as the bank invests in the business.
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Last week, Wang Hongzhang , the Chairman of China Construction Bank, the second-ranked Chinese bank by assets, said in an interview that CCB is shopping for an acquisition, most likely a bank in Europe with an international presence.
Peruvian police arrested seven suspected Peruvian militants on March 29, 2008 on the border with Ecuador as they returned to their country after participating in a meeting of the Bolivarian Continental Coordinator (CCB) which took place in Quito, Feb. 24-28.
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