Peng Shuai is a former world number one doubles player and reached 14th in the singles rankings in 2011Chinese player Peng Shuai has still not directly been in contact with the Women's Tennis Association (WTA), which says "no amount of money" would stop the tour pulling events out of China.
Peng has not been heard from since she made sexual assault allegations against a top Chinese government official.
WTA chairman Steve Simon told the BBC there will be no events in China next year without proof that Peng is safe.
"We cannot stand by compromises. This is a right and wrong issue," he said.
The WTA has been told Peng is safe, and in Beijing, by the Chinese Tennis Association, although Simon said there has been no confirmation that is true.
"I'm very very concerned about her," he said in an interview with the BBC on Friday.
Fears for 35-year-old Peng's welfare have continued to grow since she said on 3 November she was "forced" into a sexual relationship with former China vice-premier Zhang Gaoli.
Peng made the allegations in a post on Chinese social media site Weibo and they were soon deleted from China's internet.
It is the first time such a claim has been made against one of China's senior political leaders.
Simon added: "I'm very concerned about the challenges that come when somebody has the courage to step up and speak out, bringing a past experience that is tied to sexual assault or harassment.
"It takes an awful lot of courage just to get to that point - and now she's dealing with more pressures if she is hearing what is going on.
"It is critical to us that we are able to make sure she knows we are worried about her and that we're prepared to offer any level of support that she needs."
Peng is a former world number one doubles player who has won two Grand Slam titles - at Wimbledon in 2013 and the 2014 French Open, both alongside Chinese Taipei's Hsieh Su-wei.
She also achieved a career-high singles rankings of 14 in 2011 and reached the US Open singles semi-finals in 2014.
Earlier this week, Chinese state media released an email attributed to Peng, but Simon cast doubt about its authenticity.
Talking to BBC tennis correspondent Russell Fuller, Simon said he did not believe speaking out strongly and demanding answers from the Chinese authorities would be counterproductive.
"Diplomacy is always very very strong and I am sure that they would prefer we are not talking about this," he said.
"I think we are better addressing it than working in a vacuum where nobody knows and the world is trying to figure out our position.
"I'm very comfortable with the approach that we have taken right now, and we'll continue to do it in a very respectful and hopefully responsible way."
WTA prepared to pull tournaments out of China
The WTA has heavily relied on Chinese investment in its players' tour, leading to a number of lucrative tournaments and the season-ending finals being held in the country over recent years.
But Simon said assurances about Peng's safety and a transparent investigation into her allegations were of paramount importance to the WTA, not the financial implications of potentially pulling events out of China if these conditions are not met.
"This is not about the money, this is about doing what is right and making sure Peng Shuai is safe and free," added Simon.
"The sad part about this is that we have some tremendous partners and some tremendous friendships in China.
"We don't want to be in this position, but at the end of the day this is one of those decisions where compromises are not acceptable.
"We have to do what is right here and we will figure that out if we end up being in that position at the end of the day."
Ros Atkins on...the missing Chinese tennis star Peng ShuaiStars speak out as people ask #WhereIsPengShuai
Serena Williams, Novak Djokovic and Andy Murray have been among those who have expressed their concerns about Peng's whereabouts.
People from across tennis - including past and present players, coaches and journalists - have been demanding answers about Peng's welfare, as have other high-profile sports stars, actors and politicians.
Many have been using #WhereIsPengShuai on Twitter posts, along with a photo of her.
The Lawn Tennis Association, the sport's governing body in the United Kingdom, said it has "offered assistance" to the WTA to "establish the safety and wellbeing" of Peng.
The United Nations says it wants proof of Peng's whereabouts and has urged the need for an investigation "with full transparency".
Analysis
Russell Fuller, BBC tennis correspondent
Pulling out of China would have significant repercussions for the finances of the WTA Tour, the earnings of its players and the spread of the sport among the country's 1.4 billion inhabitants.
Steve Simon disputes the Tour has put too many eggs in one basket, but there are usually 10 Chinese events a year on the WTA schedule. Many are very lucrative.
The last time the WTA Finals were able to take place in Shenzhen, in 2019, there was $14m in prize money.
And 15 of the world's top 20 did not make their way to Wuhan, barely two weeks after the conclusion of the 2019 US Open, just to visit the birthplace of Li Na.
The financial loss would cut deep. But Simon believes that on this issue "compromises are not acceptable".
