The billionaire's sportswear and fashion retail company, Frasers Group Plc, notified Asos on Friday that it had become a significant shareholder in the company, the report said.
The move makes Frasers the fourth-biggest shareholder in Asos.
According to the newspaper, Frasers is seeking to use its stake in the online retailer to build a partnership as Asos recently announced an overhaul of its business model.
Asos on Wednesday vowed to revamp its supply chain, better leverage its data and cut costs as a sharp downturn in the economy has badly affected its business.
Several retailers in Britain have warned about their profit outlooks as they face higher energy and staff costs and a weak pound.
Ashley stepped down as a director at Frasers last month. He still retains about 69% of the company's controlling equity.
Frasers and Asos did not immediately respond to requests for comment.
(Reporting by Akanksha Khushi in Bengaluru; Editing by Matthew Lewis)
