US venture capitalist company Kohlberg Kravis Roberts (KKR) is rumoured to be mulling a bid for UK-based J Sainsbury if the supermarket firm's new chief executive fails to produce signs of a turnaround soon.

Last week Justin King took up the post of CEO of Sainsbury's, which has been losing market share to its main rivals and has lost its place as the second-largest UK grocery retailer to Wal-Mart's Asda.

Rumours have been circulating about potential bidders for Sainsbury's for many months, but the founding family, which control 38% of the company's shares, are believed to be becoming more likely to consider an offer, reported the Guardian, citing retail insiders.

KKR, which considered a bid for UK grocer Safeway last year, recently asked investors for US$3bn to finance European takeovers.