Cook will meet with senior Chinese government and Communist party leaders, according to Reuters, which cited an unnamed person. The Chinese officials include people in charge of propaganda, the report said.
China has proved difficult for Apple over the last couple of months. Last month, the country shut down Apple's iTunes movie and book services after just seven months of operation. Also in April, Apple reported its first drop in iPhone sales, driven in part by a 26 percent fall in sales in Greater China to $12.5 billion.
Billionaire investor Carl Icahn last week sold his stake in Apple, citing concerns about China.
Apple didn't immediately respond to a request for comment.