Sports Direct's announcement comes days after Blacks Leisure said it has received an expression of interest from Sports Direct.
Sports Direct's majority shareholder is Mike Ashley, the owner of Newcastle United.
Sports Direct has informed the City that "Further to these announcements and after careful consideration, notwithstanding that Sports Direct remains a committed and supportive shareholder of Blacks Leisure, Sports Direct has decided not to proceed with an offer for Blacks Leisure."
Sports Direct is the largest shareholder in Blacks, holding a 21.3% stake.
Blacks, which owns 98 Blacks outlets, 208 Millets stores and the Peter Storm and Eurohike brands, put itself up for sale earlier this month, as it grappled with a £36m debt pile.
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