The grocer is valued at£7.6 billion, but market sources said that a bid would need to reach£10 billion to be successful.
Last week, the grocer's stock market value rocketed by more than£1 billion, as three large private equity groups revealed they were considering a bid.
In a statement to the stock exchange, CVC Capital Partners, Kohlberg Kravis Roberts (KKR) and The Blackstone Group International said that they were only at the 'preliminary stages' of assessing a bid.
Sainsbury's said that no proposal had been received and it had no further comment to make.
Private investment firm Texas Pacific Group is understood to have also been circling the company.
If a takeover was successful, the new private equity owner could give Sainsbury's clothing and electronics ranges an overhaul, to up the ante against rivals including Tesco, where 20 per cent of sales come from non-food items.
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.