TK Maxx is looking likely to move into the old four-storey New Look unit on Oxford Street.
Last month they reported a 10.6% increase in annual turnover. This comes as it opened as many as 23 stores across the UK.
The new 30,000 square foot store will add to its existing central London portfolio, with three stores located in the City, Covent Garden and Kensington.
The company has signed a 10 year lease and will pay £2.5 million a year for the unit.