Beijing wants 75 percent of technology products used by China's financial institutions "secure and controllable" by 2019, the paper reported, citing an official document expected to be circulated to businesses in the next few months.
The new rules have aggravated concerns among foreign companies that Chinese authorities are trying to force them out of the country, the Times said.
Approved by authorities late last year, the rules do not specify what is meant by "secure and controllable", the paper added.
Source code - the usually tightly guarded commands that create programmes - for most computing and networking equipment would have to be turned over to officials, according to the incoming regulations.
Firms planning to sell computer equipment to Chinese banks would have to set up research and development centres in the country, get permits for workers servicing technology equipment and build "ports" which enable Chinese officials to manage and monitor data processed by their hardware.
It quoted a letter sent on Wednesday to a top-level Communist Party committee on cybersecurity from foreign business groups, including the U.S. Chamber of Commerce, accusing them of protectionism.
The letter called for "urgent discussion and dialogue" about policies forcing Chinese companies to use only technology developed and controlled by Chinese firms.