Private equity outfit Carlyle Group has served up an offer with Chinese state group CITIC, while TPG Capital is working with local firm Wemart Stores for the outlets, which could be worth up to $3bn.
The global fast food giant is offering a 20-year master franchise agreement to potential buyers, with the option of extending it by another decade.
House of Fraser owner Sanpower Group has also made an offer for restaurants, Reuters reported being told by sources.
One of the sources said the Carlyle-CITIC consortium was the likely frontrunner to win the auction.
In April, it was widely reported that McDonald's was targeting private equity firms for the sale, including Bain Capital, MBK Partners and TPG.
The company announced its long-term goal in March to become around 95 per cent franchised in China, Hong Kong and South Korea.
Around 2,800 of its restaurants are located in the countries. The South Korea sale is being run separately.
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McDonald's intends to open more than 1,500 branches in the three countries over the next five years and will also start to identify strategic partners in Japan and Taiwan.
The firm has also pledged to create 5,000 new jobs in the UK by the end of next year.
Carlyle and TPG declined to comment. McDonald's has been contacted for comment.