The informal approach is worth 610p a share, according to reports in the Financial Times.
Sainsbury's this morning confirmed that it had received an approach “which may or may not lead to an offer being made”.
“The board will make a further announcement, as appropriate, in due course,” it added.
In a statement, Delta Two confirmed it was in preliminary discussions with the retailer. "These discussions relate to the possibility of Delta Two increasing its interest in Sainsbury by way of a cash offer to acquire the balance of the ordinary share capital of Sainsbury," it said.
Delta Two owns a 25% stake in Sainsbury's. Its CEO Paul Taylor flew members of the Sainsbury's family to Sardinia at the end of last week to make the informal approach, according to the Financial Times.
However, further reports add that if a bid is unsuccessful, Delta Two could consider putting pressure on Sainsbury's to restructure its property portfolio. In May, Sainsbury's chairman Philip Hampton said the retailer would retain its property following pressure from shareholders to release some of the value of its £8.6bn portfolio.
Sainsbury's has been the centre of takeover activity for some months. In April it fought off an approach from a private equity consortium including CVC Capital Partners, The Blackstone Group International and TPG Capital.