Mike Ashley's Sports Direct has called for wide-ranging investigation into the sportswear industry, complaining about the dominance and Adidas and Nike.
The firm said the "must-have" brands hold a bargaining position which allows them to control supply and the price of their products.
Sportswear giant Adidas has blocked Mr Ashley's retail empire from selling some of its products, Sports Direct said.
"Sports Direct believes that the industry as a whole would benefit from a wide market review by the appropriate authorities in both the UK and Europe," it said in a statement.
Mr Ashley's grievance stretches as far back as 2013 when the German giant withdrew replica Chelsea shirts from Sports Direct stores.
The retailer said the dominance of Nike and Adidas allows them to "[refuse] to supply key products ... with no apparent justification".
The calls come after the Sunday Times revealed that Nike has told several independent retailers it will pull its products from their stores.
It is part of a move by the US giant to reduce the number of retailers it uses and push customers towards its website.
"All those companies that built a business on the back of Nike and Adidas are toast - there's no way they can replace that [business]," a source told the paper.
Last month, Sports Direct complained that its rival JD Sports' planned £90 million takeover of Footasylum could reduce Mr Ashley's access to the top brands.
In the past, Adidas and Nike have preferred to work with JD Sports, but Sports Direct has attempted to make inroads, appointing former Nike executive David Daly as chairman of the its board.
"Sports Direct has consistently aimed to provide the widest range of products at attractive prices and will continue to work constructively with all its suppliers to enhance its product offering for the benefit of consumers," the company said on Monday.
