Negotiations between the parties ended in the last few weeks according to Reuters, which cited three people with knowledge of the matter.
TPG Capital and Leonard Green & Partners bought into J Crew through a $2.8bn deal in 2011, and we hoping to pull in $5bn from an exit.
J Crew has more than 450 stores and about $2.4bn in annual sales.
Bloomberg previously suggested the public listing would take place in the US.
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