The actor, who has appeared in the X-Men and Iron Man film franchises, disappeared three months ago after she was accused of receiving an under-the-table payment for a major film role in China.
Analysts now believe Ms Fan could be the victim of a government crackdown on “yin yang contracts” – a form of tax evasion in the entertainment industry in which large fees are hidden from official records.
Jonathan Landreth, former Beijing-based Asia editor for The Hollywood Reporter, said arresting Ms Fan could be a way to send a clear signal to the rest of the industry in China.
“It has long been an open secret that a movie budget is a great place to hide money,” he told CNN.
“Maybe this is just scaring folk to ... start paying taxes. If someone were to get busted, then I think it would send a ripple effect to how film production goes forward in the coming years.”
The star, who has 62 million followers on social media, has not been seen in public since visiting a children’s hospital at the beginning of July.
She stopped posting on China’s most popular social media platform Weibo on 26 July.
In May, a former host for state-run China Central Television posted pictures of two contracts allegedly tied to Ms Fan’s 2003 film Cell Phone.
One of the apparent contracts showed an official salary of $1.6m (£1.2m), according to CNBC. The other indicated she had received unofficial additional payments of $7.8m.
Ms Fan’s representatives denied she had taken undeclared payments, but the accusation led to a wider state investigation into the entertainment industry.
Earlier this month Securities Daily, a Chinese state-run publication, stated Ms Fan had been brought “under control and about to receive legal judgment”.
The article was quickly removed from the publication’s website and Chinese authorities have since refused to comment on whether the actor has been arrested.
Several companies have cancelled commercial deals with the high-profile celebrity since the allegations emerged.
The missing actor was given a 0 per cent rating for “social responsibility” by the authorities at Beijing Normal University last week, adding to speculation she had fallen out of favour with the Chinese government.
“If you are a billionaire, then that is something that obviously you can enjoy to a certain extent, but you’ve got to be very, very wary that you don’t at any stage cross a red line of some sort and fall afoul of the Chinese Communist Party,” Fergus Ryan, an analyst at the Australian Strategic Policy Institute, told CNN.
The star, who turned 37 on Sunday, topped Forbes’ China rich list for entertainers last year, with earnings estimated to be more than $43m.
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