Sky News has learnt that Gymshark has been holding preliminary talks with institutional investors and investment banks about a flotation.
A decision to press ahead with a listing could still be some way off, but if it does happen, it would be among the most eagerly awaited of a British consumer-facing company for some time.
The brand was founded by Ben Francis in 2012 in his parents' garage in Birmingham, and has quickly become an international success story, with customers in more than 130 countries.
Gymshark has built a huge customer base among millennials, with millions of followers on Facebook and Instagram.
It sells lifestyle apparel and accessories, and has ambitions to expand into a much broader range of health-related products.
City sources say it has been "aggressively" pitched to by investment banks in recent months, and has signalled its interest in pursuing an initial public offering of its shares, probably in London.
One person close to the situation suggested an announcement could come in the next few months, although the recent performance of London-listed online retail stocks, such as ASOS, Boohoo and THG Holdings, owner of The Hut Group, has created an underwhelming environment for digital consumer brands to go public.
In August last year, Mr Francis orchestrated the sale of a 21% stake to General Atlantic, the private equity firm.
He retains a controlling stake in the company, making him one of Britain's wealthiest people under 30.
The timing and size of a flotation have yet to be decided, and one source close to General Atlantic insisted that there was little prospect of an imminent announcement.
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The brand's marketing is largely founded on its use of social media influencers, with sales undertaken directly to consumers through digital channels - although it briefly opened a pop-up store in central London last year.
Mr Francis recently reassumed the role of chief executive from Steve Hewitt, a former Reebok executive, who was recruited in 2015.
He was briefly a member of Theresa May's business advisory group during her tenure as prime minister.
The entrepreneur has set his sights on challenging global sportswear giants like Adidas and Nike.
During a recent discussion with executives from Goldman Sachs, the transcript of which was published by the US investment bank, he drew comparisons with Amazon and Apple.
"There's this ecosystem of products that support the ambitions and goals of their consumers," he said.
"I want Gymshark to be like that [and] in 10 years' time, I would love us to be sat here and shuffling about the time that Gymshark, let's say, only sold apparel and accessories.
"I want Gymshark to be the fitness brand [and] I want Gymshark to be playing a larger part of people's fitness journeys, both mental and physical."
A Gymshark spokesperson said: "We regularly speak to financial institutions to ensure we are connected to the business world and we continue to learn.
"Any recent conversations we have had have been about introducing these organisations to Gymshark and our journey so far."
A spokesman for General Atlantic added: "We are working with Ben and the team to build Gymshark into the global leader we know it can be."