The South African company pursuing Argos owner Home Retail (LON:HRG) has also made an approach to former Comet owner Darty, it emerged on Wednesday.
Steinhoff International, which owns furnishing retailers Harveys and Bensons for Beds in the UK, has proposed to acquire the London-listed French electronics retailer for 125p per share.
Rival French stationery and electronics retailer Fnac made a £558mln offer last year for Darty, which used to be called Kesa Electricals and sold now-collapsed UK electrical retailer Comet in 2011.
Darty said it had received the latest approach from Steinhoff's French electrical and home furnishing arm Conforama, whom it said was not certain to make a firm offer.
Darty said in a statement: "The board will issue a further statement if and when appropriate. In the meantime, Darty shareholders are advised to take no action."
Steinhoff made a potential 175p per share offer for Home Retail, which has already agreed a proposed £1.3bn takeover by supermarket chain Sainsbury's, earlier this month.