According to the Business newspaper, the banks both want to list their entire operations on the Chinese mainland exchange in order to encourage greater investment from the Chinese, although the plans have seen opposition from market regulators.
Under current Chinese rules, foreign banks are not allowed to list in China, although large foreign conglomerates are allowed to have their China-based operations listed.
For HSBC, however, this is likely to be an unattractive option due to the small scale of their Chinese business.
The request has been seen by some as a test of China's flexibility on its rules on foreign financial firms, with progressive deregulation of the mainland market expected in the near future.
The Chinese are required by World Trade Organization rules to open up their financial sector.