PRAGUE, June 23 (Reuters) - Any restructuring of CEZ must benefit shareholders in the majority state-owned Czech utility and no concrete proposals are yet available, the company said on Thursday.

Prime Minister Petr Fiala said on Wednesday the state, which owns 70% of CEZ, wanted "to get under control in the near future the whole network of key domestic power plants" in its energy strategy. Analysts said this suggested CEZ would be split.

Government officials previously said talks were underway on the possible restructuring of CEZ, central Europe's biggest listed utility.

In 2018, a previous government discussed splitting CEZ into separate groups for energy assets such as coal and nuclear plants and newer assets such as renewables.

"There is no proposal for a specific form yet," CEZ said in an email. "It is a matter for shareholders."

"Any transformation must be beneficial to shareholders. Otherwise it isn't possible," it said, adding that any possible modifications would aim to streamline the group's structure.

CEZ said in its response to Reuters questions that it would provide an update on its business activities at its annual shareholder meeting next week.

The government office and Finance Ministry, which manages the state's stake, did not immediately reply to requests for comment.

Komercni Banka analysts suggested a restructuring could involve the state gaining control of conventional power plants, which would mean buying out minority shareholders, likely at a premium.

CEZ shares have climbed 84% in the past year amid heightened dividends and as rising wholesale prices boost profits. Shares traded down 1.4% on Thursday, caught in global selling pressure.

CEZ is the country's dominant electricity producer and operates its only nuclear power stations, which Fiala said remained a key part of the energy mix.

The Czech Republic has surplus electricity production but is a big oil and gas importer, making it vulnerable should Russia cut off gas supplies completely. Like elsewhere, Czech households and firms have seen soaring electricity bills.

(Reporting by Robert Muller and Jason Hovet; editing by Jason Neely and Edmund Blair)