Shein is set for a £50 billion stock market flotation, making it one of the biggest in the history of the London Stock Exchange.
Both the government and Labour have held talks with the online fashion brand, which was set up in Nanjing in China but is now based in Singapore, to try to persuade it to float in the UK amid intense interest from New York and Paris, The Week reported.
The company could file for an initial public offering (IPO). And doing so in the UK would be a "much-needed milestone for ministers and City chiefs who have been battling to restore London's status as a global listing venue after a series of blows", The Times reported.
Launched in 2008, the "ultra-fast" fashion retailer has seen its popularity explode over the past decade. It has expanded rapidly around the world while buying up many of its rivals. For Gen Z shoppers - those under 30 - Shein is now the hottest ticket in town.
The Shein business model revolves around "low-cost, throwaway items that are constantly being marked down.
With roughly 10,000 new products released per day, its "entire premise is based on fashion being disposable, the implication being: here, buy these very cheap and often poorly made clothes, wear them once, then buy something else. And as wild as that may seem to some, it's a modus operandi that is clearly working."
Young shoppers in particular have been "enticed away from rivals such as Boohoo and Asos thanks to ultra-cheap prices" that include less than £3 for a top or £4 for a dress.
