Retail veteran Greg Tufnell is said to be fronting the bid, which the BBC said was believed to be the best offer received so far for the company bought by Sir Philip Green for £1 in 2010.
Earlier this month, Tufnell, who is the brother of former English cricket Phil, registered a new firm, Richess Group, at Companies House.
Its other directors are Nick de Scossa, a Swiss banker, and Lisbon-based entrepreneur José Maria Soares Bento.
The money for the bid is said to come from Soares dos Santos, who is closely linked to Soares Bento, and who is listed as one of Portugal’s richest people.
He currently controls supermarket chain Pingo Doce and the Recheio cash-and-carry business. The 164-store BHS chain includes about 40 loss-making shops.