Neil O'Brien - co-founder of the China Research Group of Tory MPs - said the intelligence services should publish a report into the matter.
President Trump is threatening to ban TikTok in the US.
This has forced the app to ditch plans to establish its headquarters there.
TikTok had been expected to pick California or New York - where it already has offices - after appointing an American ex-Disney executive as its chief executive in May.
However, the US president has since given it an ultimatum to sell its local business to an American firm.
"I set a date of around 15 September, at which point it's going to be out of business in the United States... unless Microsoft or somebody else is able to buy it and work out a deal," said Donald Trump on Monday.
He added that "a very substantial portion of that price" should go to the US Treasury "because we're making it possible for this deal to happen".
Microsoft has confirmed it is in talks to buy TikTok's service in the US, Canada, Australia and New Zealand - all the members of the Five Eyes intelligence alliance, except the UK.
The app's Chinese parent company Bytedance has confirmed this had forced a rethink.
"In light of the current situation, Bytedance has been evaluating the possibility of establishing TikTok's headquarters outside of the US, to better serve our global users," it said in a brief statement.
The Sun newspaper had reported on the weekend that the UK government had already approved TikTok setting up its HQ in London, and an announcement would be made this week.
However a source told the BBC that Bytedance had yet to make a final decision, although London was on a short list of possibilities.
Dublin and Singapore have been reported to be the other options.
A spokesman for the Prime Minister said any decision would be a "commercial one" taken by Bytedance, and added that Boris Johnson had not discussed the issue with President Trump.
The China Research Group represents a group of about 50 MPs who are concerned about Beijing's influence in the UK.
It previously helped pressure the government into a rethink on Huawei, and has also raised concerns about plans to let Chinese companies invest in UK nuclear power stations.
Mr O'Brien said he was not opposed in principle to the idea of TikTok being based in London, but said a "deep dive" into its code should be carried out first.
"It would be useful for the government to use the kind of specialists in cyber-security that only it has access to, to give us a definitive view of whether the app is safe," he told the BBC.
"[If it is] we should welcome investment by TikTok in the country.
"But if there are problems, as some media reports have suggested, with either political interference in its algorithms and the content that's shown, or about where the data is ending up and a lack of security - well that would raise a whole bunch of other questions."
TikTok has said that it strictly abides by local laws.
It currently stores data from its international users on servers based in the US and Singapore. This keeps it separate from that of users in mainland China, who use TikTok's sister app Douyin.
While the government has not commented on a security review, as a matter of course GCHQ looks into any cyber-issue flagged as a national security threat by the US.
Two points are believed to be of particular concern to the agency.
Firstly, whether Chinese spies could get access to the geo-location data - including GPS coordinates and internet addresses - logged by the app.
Secondly, the degree to which the app could be subverted to push certain political content at users.
While TikTok says it would not send international users' data back to China, there is concern it would be compelled to do so if Beijing invoked its National Intelligence Law.
It obligates Chinese citizens to "support, assist and cooperate" with the country's intelligence services and to keep such activity secret.
Such concerns have to be weighed against the prestige of hosting TikTok's headquarters, and the degree to which doing so might help repair relations with Beijing following a ban of the use of Huawei's 5G kit.
"If TikTok decided to base its new HQ in London, it would certainly cement it as a global tech hub," commented Chloe Colliver from the Institute of Strategic Dialogue think tank.
"There are already some very prominent start-ups, but TikTok is one of the fastest growing tech companies in the world."
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