In a brief statement Blacks said that it had held talks with Jeronimo Martins, the Portuguese supermarkets group "regarding the possible development of Jeronimo Martins' operations in UK sports retail", although it stressed that the talks were "non-exclusive" and "exploratory".
Martins is believed to be seeking a buyer for a majority stake in Lillywhites, best known for its flagship store in London's Piccadilly Circus. It paid Forte, the hotels group, pounds 28.5m for the stores in 1995.
Analysts said Blacks might be keen to expand Lillywhites, which has 10 stores dotted around the country, by opening concessions in its existing First Sport or Blacks Outdoor formats.
"Lillywhites would be a good name to have in their store portfolio," said Williams de Broe analyst Jeremy Hilditch. "But with strong London brands you have to be careful about pushing them out elsewhere."
Opening in-store concessions has worked for Hamleys, the toy retailer, allowing it to expand from its flagship store on London's Regent Street.
Lillywhites may also be attractive for its strength in selling sports equipment. Successful sports retailers of recent years such as Blacks and JJB Sports have tended to concentrate on selling clothing - especially football strips - and shoes.
However, demand has fallen away recently, prompting worries that wearing sports gear is no longer considered fashionable.
Lillywhites stocks a wide range of equipment such as tennis rackets, cricket bats, skis and exercise machines, demand for which is less vulnerable to the whims of fashion.
The group has not been without its problems, however, suffering the departure of several top managers in 1996.
Blacks shares firmed 1p to 370p. Since the beginning of the year they have slipped from a high of 518p.