CVC Capital Partners, Kohlberg Kravis Roberts and The Blackstone Group International said they were at the 'preliminary stages' of assessing an offer in a statement to the stock exchange this month.
Cinven had been in talks with Texas Pacific for a rival consortium bid, estimated at about£10 billion. Texas Pacific has now joined the CVC-led group, leaving Cinven without a partner.
However, there is speculation that former Asda chiefs Allan Leighton and Archie Norman have been approached by a private equity consortium to lead a multimillion-pound takeover bid for the UK's third largest supermarket chain.
However, Sainsbury's might also consider selling its vast property portfolio to prevent a takeover, if interest from private equity groups turns into a formal offer.