The entrepreneur is reportedly vying with Sports Direct and JD Sports, as well as one unknown company to purchase the struggling business.
The deadline for any bids to be made is today and KPMG – which is handling the auction process – could reportedly name its preferred bidder today as well.
A spokesperson for KPMG confirmed the identity of the three bidders hoping to secure the deal but admitted the fourth apparently remains a mystery.
Sky News originally reported Jones had tabled a bid for the chain which, last month, admitted it needed to find a buyer to safeguard its future.
It is believed the sale of Blacks would take the form of a pre-pack administration in an attempt to quickly revive the company’s fortunes as quickly as possible.
Last month, Sports Direct – which is majority-controlled by Newcastle FC owner Mike Ashley – was thought to have pulled out of the running for the group.
Scottish clothing group Edinburgh Woollen Mill has also been linked with the purchase of the company.
Blacks reported a £16m loss for the six months to August 27 last year – almost double the loss made for the same period in 2010.
The retailer – which owns 98 Blacks outlets, 208 Millets stores, as well as the Peter Storm and Eurohike brands - employs some 3500 people.
By Andy Pearce