“However, the way that we would describe it is that these jobs tend to have a defined amount of runway and Simon seems, to most senior people in the NHS, to be on the final stretch of his particular runway. It would therefore not surprise us if this winter proved to be the last in his current position.”

Another Government source told the Mail on Sunday: “Simon has been doing the job since 2014, which is longer than most of his predecessors, and talks are under way about a new role in the public sector.”

Both newspapers reported that Baroness Harding, former boss of the telecoms firm TalkTalk, is thought to be the favourite to replace Sir Simon despite her controversial leadership of Test and Trace and relative lack of healthcare experience.

One senior NHS source said her appointment would likely be viewed with “suspicion” by healthcare bosses, if confirmed.

“You can say what you like about Simon, but he’s been doing the job a long time and he’s well respected,” the source told The Telegraph.

“Dido on the other hand doesn’t have the same type of experience although she did chair NHS Improvement for a few years. And Test and Trace hasn’t exactly gone swimmingly. It’s not immediately apparent that she would be the best candidate for the job.”

Sir Simon, 54, has long been friends with Boris Johnson since he helped secure the Prime Minister’s election as president of the Oxford Union.

When Sir Simon was appointed to run the NHS in 2014, David Cameron claimed he “knows more about NHS problems and market solutions than any man alive”.

A spokesman for the Department of Health said the government would not comment on “speculation”.

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