The people could not be identified as the information is not yet public. Didi did not respond to a request for comment.
The books will close at 5pm in each region on Monday, the people said.
Didi set a price range of $13 to $14 per American Depositary Share (ADS), a regulatory filing showed on Thursday, and said it would offer 288 million such shares in the IPO. At the top of the range, the deal will raise $4.03 billion.
An overallotment option could see the company sell an extra 43.2 million shares to raise up to an extra $605 million.
At the flagged price range, Didi would be worth $62.4 billion to $67.2 billion.
(This story corrects to add dropped word in the second paragraph, clarifying Didi did not respond)
(Reporting by Yilei Sun in Beijing and Scott Murdoch in Hong Kong; Editing by Christopher Cushing)