The three students - freshmen LiAngelo Ball, Cody Riley and Jalen Hill - were taken into police custody on Tuesday morning for questioning and released at around 4 a.m. on Wednesday, one of the sources said.
Ball, the younger brother of National Basketball Association rookie Lonzo Ball of the Los Angeles Lakers, declined to comment when reached by phone at his hotel on Wednesday. The others could not be reached.
The University of California, Los Angeles, team is in China for its season-opener against Georgia Tech on Saturday in Shanghai.
Ball, Riley and Hill were questioned about stealing from a Louis Vuitton store during the team's visit to Hangzhou, home of the game's sponsor, e-commerce giant Alibaba Group Holding Ltd.
The sources said police had released the three on condition that they remain at their luxury hotel in Hangzhou while the legal process plays out. It was not made clear, however, how long that would take.
"There is a lot of uncertainty around how long they will need to be in that position before there's some update on the situation," said one of the sources, who declined to be identified due to the sensitivity of the situation.
Chinese authorities have up to 37 days to decide whether to pursue official approval for a formal arrest, Margaret Lewis, a law professor at Seton Hall University in New Jersey who researches China's legal system, told the Los Angeles Times.
An arrest would prompt an investigation that could take up to two additional months before prosecutors bring formal charges, Lewis told the newspaper.
From there, the process could stretch out much longer, and convictions are a near certainty in Chinese courts, which are controlled by the ruling Communist Party.
Often, however, China will deport foreigners suspected of having committed relatively minor offences without going through the whole process.
The U.S. State Department and UCLA Athletics officials declined to address how long legal proceedings might take.
A U.S. State Department official said the department was aware of reports of three American citizens being arrested in China and stood ready to provide assistance but had no further comment due to privacy considerations.
The Chinese government reported the incident to U.S. officials, Chinese foreign ministry officials have previously said.
In Beijing on Thursday, Trump met Chinese President Xi Jinping to discuss trade, North Korea and other topics. A White House official said the issue of the detained players did not come up between Trump and Xi.
In a video posted Wednesday on Twitter by ESPN writer Arash Markazi, LaVar Ball said his son LiAngelo would be fine.
The players will not play in Saturday's game against Georgia Tech, UCLA Athletics spokeswoman Shana Wilson said.
(Reporting by John Ruwitch in Shanghai, Matt Spetalnick in Beijing and Suzannah Gonzales in Chicago; Additional reporting by Arshad Mohammed in Washington; Editing by Nick Macfie and Bernadette Baum)