Former NHS Trust chairman Roy Lilley said it has been suggested to him that Sir David Nicholson will "be gone before September".
He told Daybreak: "He will be gone before the party conferences, they won't want to take this to the conferences".
On the subject of Sir David's expenses he said, "you would expect a guy like that to have high expenses", he added, "but there are some 'unexplained' expenses".
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The department store chain said nearly 400 jobs would be lost as it grapples with the pressures facing the retail sector.
Consumer prices have rocketed by 58% since 2003, with the UK industry paying the biggest bills in Europe.
Friday will be a much calmer day for many, with the weather set to remain dryer with sunny periods and much lighter winds than on Thursday.