Mobile phone network operator O2 already has a 40 per cent stake in the 300-store UK chain.
Sales at the mobile phone retailer have been disappointing during the past few months - down 21 per cent on a like-for-like basis during the second half of the year.
It is believed that DSG, which runs electricals retailers Currys, Dixons and PC World, will confirm the sale when it reveals its full-year results on Wednesday.
O2 is owned by Spanish telecoms giant Telefonica. A spokesman for the company said: 'It is no secret that, as Joint Venture partners, both parties have been in ongoing discussion with regards to The Link for some time. However, no deal has been done and we're unable to comment further at this time.'
DSG was unavailable for comment.
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