Mr Farrar, who has worked in NHS management for 30 years, said he had been 'encouraged' to apply for Sir David's job but would decline the invitation.
He will stand down from leading the NHS Confederation, which represents NHS commissioners and providers, when his two-and-a-half-year secondment from the NHS ends on 30 September.
Mr Farrar’s work will be undertaken by the chief executive of NHS Employers Dean Royles until a permanent candidate is appointed.
Mr Farrar said: ‘It has been an enormous privilege to work in the NHS for more than two decades. I have had the opportunity to lead work at the NHS Confederation, in the north west and nationally in the DH.
‘The real sense of career satisfaction is to have been able to shape and see real improvements in patient care, delivered according to need and never ability to pay.
‘I am looking forward to creating a range of new opportunities to improve health care provision in the future in the UK and overseas and delighted that I will be able to continue with some major NHS Confederation projects.’