His appointment would be an effort to deflect criticism that Delta Two has little knowledge of the retail sector, according to reports in the Guardian.
Campbell left Asda in November 2000 after 16 years at the retailer. If he did become chairman, he would be reunited with Sainsbury's CEO Justin King, who he worked with at Asda for six years.
Meanwhile, the Sunday papers were full of reports on Delta Two's bid. Former Conservative Party cabinet minister David Mellor has been advising Delta Two on the bid as a business development director, according to the Sunday Telegraph.
Delta Two will also have to raise its offer by at least £2bn in order for it to be accepted by the Sainsbury family, said reports in the Mail on Sunday. The Independent on Sunday added that Lord Sainsbury, who owns an 8% share in the retailer, is set to oppose a takeover.
Delta Two is expected to meet with the Sainsbury family this week to discuss the deal, according to reports in the Financial Times.