Richard Carey announced in October he was standing down from the health authority, which has been embroiled in a recent staffing controversy.
The post has a salary between £111,000 and £151,000.
NHS Grampian said none of the shortlisted candidates had been appointed.
This followed an "open competition involving a robust selection and interview process".
The post is currently filled by interim chief executive Malcolm Wright.
A spokesperson said: "Following an open competition involving a robust selection and interview process a decision has been taken not to appoint any of the shortlisted candidates.
"We have discussed options with the Scottish Government, and further expressions of interest in the post are now being sought. As this is an ongoing recruitment process, no further comments will be made until it is complete."
Recommendations were made in reviews last year looking at Aberdeen Royal Infirmary, the care of older people and concerns over general surgery.
NHS Grampian has failed to appoint a new chief executive after the post was advertised and candidates interviewed.