The Carlyle Group (CG) and a multinational group are speculated to be the final two bidders on the deal, according to the New York Post.
The 20-year master franchise agreement is valued between $2 billion and $3 billion.
A McDonald's spokeswoman told CNBC that McDonald's restructuring initiative announced last year involves reevaluating its ownership structures around the world.
In 2006, the Washington, D.C.-based private equity firm Carlyle Group purchased a stake in Dunkin Brands Group (DNKN), alongside other private equity firms including Bain Capital.
McDonald's total share in the Chinese fast-food market dropped to 23.9% last year, down from 40% in 2012, according to Bloomberg.
Analysts have said that McDonald's novelty is wearing off in the country, as consumers aren't concerned about its cheap prices and are shifting towards healthier options.
Separately, TheStreet Ratings objectively rated this stock according to its "risk-adjusted" total return prospect over a 12-month investment horizon. Not based on the news in any given day, the rating may differ from Jim Cramer's view or that of this articles's author. TheStreet Ratings has this to say about the recommendation:
We rate MCDONALD'S CORP as a Hold with a ratings score of C+. The primary factors that have impacted our rating are mixed - some indicating strength, some showing weaknesses, with little evidence to justify the expectation of either a positive or negative performance for this stock relative to most other stocks. The company's strengths can be seen in multiple areas, such as its notable return on equity, expanding profit margins and solid stock price performance. However, as a counter to these strengths, we also find weaknesses including unimpressive growth in net income, weak operating cash flow and generally higher debt management risk.
You can view the full analysis from the report here: MCDMCD data by YCharts