Tchenguiz, who owns a 10% stake in the retailer, does not believe the indicative offer, which values Sainsbury's at £10.6bn, is fair value. A more realistic price of 610p a share or above is more realistic, according to reports in the Financial Times.
His position is a severe blow to Delta Two, which would need his support, and that of the Sainsbury's family, to clinch the 75% acceptance it needs for the deal to go through, the reports added.
The Sainsbury's family are also understood to oppose the deal.
Reports earlier this week suggested the family had written a letter to Delta Two which said they would not back a takeover that left Sainsbury's in too much debt or sold off its property portfolio.