If FitzGerald were offered and accepted the role at the supermarket chain he would become a rival with Patrick Cescau, his successor at Unilever, who was earlier this year named a non-executive director of Tesco.
John McAdam, a Sainsbury's non-executive director, is said to have been working on a possible list of candidates following Sir Philip Hampton's decision to become chairman of Royal Bank of Scotland, according to The Times. John Peace, the former GUS chief executive, who is chairman of Burberry and Experian, has also been linked with the position.
FitzGerald is currently chairman and deputy chairman of Reuters and Thomson Reuters where he has been for over five years.
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