BEIJING — Chinese stocks rallied this week as investors hoped Beijing would soon relax its stringent Covid policy.

The Shanghai composite gained 5% during the week. The Hang Seng Index notched weekly gains of well over 8%, bouncing back from 13-year lows hit in the last two weeks.

The Chinese government has yet to announce any official policy change. Covid-related restrictions on travel, regular virus testing requirements and other measures generally remained just as tight.

However, the stock rally that accelerated Friday followed multiple unconfirmed rumors of a coming Covid policy change.

"The rally that we saw this morning was primarily triggered by the hope for reopening to happen earlier than expected," Zhiwei Zhang, president and chief economist at Pinpoint Asset Management, said Friday on CNBC's "Capital Connection."

Zhang pointed to a closed-door speech Friday morning by a chief scientist at the Chinese Center for Disease Control and Prevention that suggested a transition away from zero-Covid policy could happen soon.

CNBC was unable to verify comments made in the speech. The disease control center and National Health Commission did not immediately respond to a request for comment.

Chinese financial media Cailian Press reported that officials would hold a press conference Saturday afternoon at the National Health Commission building on virus control and prevention measures.

The controls and continued Covid outbreaks have remained a drag on China's economy, which grew by just 3% in the first three quarters of the year from a year ago. Economists have cut their forecasts for growth next year on expectations the restrictions persist, while the rest of the world has shifted to a "live with Covid" approach.

On Monday, mainland China did mark the end of a period of heightened Covid restrictions due to the Mid-Autumn Festival in September, the National Holiday in early October and the ruling Chinese Communist Party's 20th National Congress in late October.

This week, some official descriptions of Covid included notable mentions of how the virus was "self-limiting" and controllable.

However, China's Communist Party newspaper People's Daily maintained that isolation was still necessary.

The National Health Commission also affirmed its adherence to what's officially called the dynamic zero-Covid policy.

"The clearest signal has been given. In the near term, China will stick to its unbending commitment and zero-tolerance approach, pursuing zero-Covid position as one of the world's strictest virus elimination policies," said Bruce Pang, chief economist and head of research for Greater China at JLL.

"But in the long run, China is expected to continue to make its Covid response more scientific and targeted, leading to more softened policy stance, flexible measures and gradually loose[r] restrictions," he said.

Pang doesn't expect the policy to be dropped until the end of June 2023 at the earliest.

This week's market rumors have not provided new specifics on the timing of any changes.

Pinpoint's Zhang added that also helping Friday's stock rally was a midday Bloomberg report, citing sources, that indicated U.S.-listed Chinese stocks such as Alibaba could stay listed on U.S. exchanges.

The China Securities Regulatory Commission, Ministry of Finance and U.S. Public Company Accounting Oversight Board did not immediately respond to CNBC requests for comment.

— CNBC's Sam Vadas and Abigail Ng contributed to this report.