The fashion retailer has applied to merge the two units once occupied by Dorothy Perkins and Topshop, but which are now vacant.
An application has been submitted to Wakefield Council's planning department for shop-front alterations.
However, TK Maxx has not confirmed what the future holds for its existing store in The Ridings. The Express has contacted the company for clarification.
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Should it close, it would be another blow for The Ridings which has numerous empty units and has been up for sale since last year.
There is now talk that part of the shopping centre, which was opened in 1983, could even be demolished. Read the full story here.