M&S is understood to be aiming to replace retiring chairman Robert Swannell as early as the annual shareholder meeting in July, according to a report in the Mail on Sunday.
Mr Norman was credited, alongside serial entrepreneur Allan Leighton, with turning around the fortunes of the Leeds-based supermarket chain Asda in the 1990s.
A spokesman for M&S told The Yorkshire Post: “We wouldn’t comment on rumour or speculation.
“As announced in December, our chairman intends to retire in 2017. The search for his successor is underway.”