Skims is understood to be in talks to take on the flagship store at 245 Regent Street, which has been vacant since August when Ted Baker closed its 31 remaining stores across the UK.
If the deal goes ahead, it will become Skims' first physical store in the UK. The brand opened its first permanent retail site in Georgetown, Washington DC, in June. The 3,300 sq ft store will be followed by four more locations in Florida, Texas and Georgia.
TV star and entrepreneur Kardashian launched Skims in 2019 with Jens and Emma Grede. The business was valued at $4bn (£3.1bn) after a 2023 funding round led by Wellington Management.
It is stocked in Harrods, Selfridges and End in the UK, Brown Thomas in Dublin and Galeries Lafayette in Paris.
The Crown Estate, which owns Regent Street, declined to comment, while Skims did not respond to Drapers' request for comment.