"Only if you want your private information in the hands of the Chinese Communist Party," he replied.
Asked if he would ban Chinese apps - including TikTok - he said: "I don't want to get out in front of the president, but it's something we're looking at".
That is a very worrying statement for TikTok.
The huge Chinese social media company has experienced phenomenal growth in the last three years. It's been downloaded more than two billion times.
But around the world, and not just in the US, TikTok is facing a backlash.
It's finding out the hard way that being international, a tech company, and Chinese isn't a great combination right now.
By far its largest market, India, banned TikTok last week, along with 58 other Chinese apps.
Officially security concerns were given as the reason, but that isn't the whole story.
Two weeks before, a border skirmish on India's northern frontier with China left 20 Indian soldiers dead. It's not known how many Chinese troops were killed.
The fighting was said to be gruesome, hand-to-hand combat.
Anti-China protests have grown in India in recent weeks
Thousands of miles away, Mr Pompeo said he welcomed India's move to ban the apps. They "serve as appendages of the Chinese Communist Party's surveillance state", he said.
It was a pretty extraordinary statement that flew relatively under the radar. The US government had congratulated the banning of TikTok in another country.
"Good to see India ban 59 popular apps owned by Chinese firm," tweeted Nikki Haley, the former US ambassador to the United Nations.
Much of this can be linked to Huawei, says James Sullivan, head of cyber research at British security think-tank Rusi.
"Huawei is the test case," he says. "It's probably the start of a trend in the West where sanctions will seek to squeeze, or even sink, large Chinese tech companies"
Distance from China
That has made TikTok extremely nervous, and explains its energetic and painstaking attempts to distance itself from China.
Monday saw TikTok announce it would quit Hong Kong "within days" after a new National Security Law was brought in.
The announcement came after Twitter, Facebook and WhatsApp said they would not hand over data to the Hong Kong government.
This was more than a statement from TikTok though - it was a grand gesture. A clear neon-lit sign that says: "TikTok is not close to the Chinese government."
It's a strategy TikTok has been following for quite some time.
Earlier this year it hired an American chief executive, Kevin Mayer.
TikTok is also keen to play up the localised nature of the platform, highlighting its big offices in places like London and Los Angeles.
'We would not comply'
TikTok also says it would never share data with China.
On Friday, Mr Mayer wrote a letter to the Indian government.
"I can confirm that the Chinese government has never made a request to us for the TikTok data of Indian users," he said.
"If we do ever receive such a request in the future, we would not comply."
But it hasn't won over the doubters.
"TikTok must go and it should have been gone yesterday," tweeted one Republican congressman last week following the Indian ban. This is not an uncommon view in the party.
"It is an incredibly difficult moment for the Chinese tech companies," says Dr Yu Jie from internal relations think-tank Chatham House.
"Ultimately, all of these Chinese companies would wish to set up a foothold in the US and Europe. But they've been caught up in global geo-political rivalry."
Already the sharks are circling. Facebook is pushing its Instagram Reels feature , which lets you post fun 15-second videos, in India and elsewhere. Sound familiar?
Indian companies with similar platforms to TikTok have seen a spike in downloads since the ban.
TikTok is not Huawei. It's not building the infrastructure of 5G - it's a social media company.
But its links to China means that they are often mentioned in the same breath.
In his interview with Fox News, Mr Pompeo made the direct comparison between TikTok and Huawei.
"With respect to Chinese apps on peoples' cellphones, I can assure you the US will get this right too," he said.
James Sullivan of Rusi believes security issues need to be looked at separately to actions based on sanctioning China.
"There are technical security concerns with companies like Huawei, but they shouldn't be conflated with sanctions that are based around Chinese foreign policy decisions," he said.
That is India's TikTok ban in a nutshell. A decision that is officially based around security which is also designed to punish China.
It's also pretty clear that the US is looking to hurt China too, and focusing on its tech sector could be a lever it decides to pull.
Chinese companies like Tencent - one of the world's largest gaming companies - and Alibaba will also be worried.
But it's TikTok that is now fighting for its life. Frozen out of its biggest market, India, it now faces the prospect of losing the US - another huge market for the company.
And hostility is picking up in other countries too. In Australia on Monday, the deputy chairman of the foreign Interference through social media inquiry, said TikTok might be "a data collection service disguised as social media".
"We have no higher priority than promoting a safe and secure app experience for our users. We have never provided user data to the Chinese government, nor would we do so if asked," TikTok said in a statement to Reuters news agency.
TikTok may be designed for fun and laughter, but there are politicians who are deadly serious about banning the app. As long as China and the West's relationship remains frosty, that's unlikely to change.