The grocer confirmed it has received a preliminary approach that 'may or may not' lead to an offer being made.
It is understood that Delta Two has made a tentative 610p-a-share offer for the retailer.
Last month, Delta Two fuelled speculation of a possible takeover by upping its stake in Sainsbury's to 25 per cent. Subsequently, property tycoon Robert Tchenguiz doubled his stake to 11 per cent.
In April, an earlier bid for Sainsbury's by private equity firm CVC was rejected. The Sainsbury family, which controls about 18 per cent of shares, is understood to have felt the 582p-a-share offer undervalued the retailer.
The family is understood to be unwilling to consider offers below 600p a share. It is reported that the family has given the Delta Two bid a similarly cool reception.
Delta Two is thought to want to retain chief executive Justin King and his senior management team, should the offer be accepted.
Sainsbury's said in a statement that it would make a further announcement 'as appropriate, in due course'.