Prof Murdoch resigned on June 14, after being on sick leave since March.
He was appointed in February 2022, succeeding Prof Harlene Hayne, who stepped down after 10 years in the role.
Prof Helen Nicholson has been acting vice-chancellor since March 2023.
Prof Murdoch, who had previously been the head of the university’s Christchurch campus, has since returned as a distinguished professor.
On Thursday, the university issued a statement from chancellor Stephen Higgs.
Mr Higgs said the university council was nearing the end of a consultation phase with stakeholder groups, including staff, students, mana whenua, and unions.
Consultation closes on August 31, he said.
"A position description will be finalised by council and advertising and the search process will begin shortly after.
"We are looking forward to working with the university community over the next few months on this important process," Mr Higgs said.
The financially-troubled university is seeking to make savings through a variety of "management of change" processes, and earlier this year, 107 staff accepted voluntary redundancy.
Protect Otago Action Group (POAG) spokeswoman Natasha Hope-Johnstone said a protracted hiring process is "welcome, provided the input and consultation from the university and broader community is genuinely taken into consideration".
"The post-1990s paradigm of vice-chancellors as autocratic chief executives has been a demonstrable failure as a project.
"The vice-chancellor role should be one of a senior colleague, such as the principal role in our school system, not a wildly overpaid and borderline autocratic role," Ms Hope-Johnstone said.
Ms Hope-Johnstone said the next vice-chancellor must "advocate publicly and vociferously for free, quality education as a public good".
Tertiary Education Union co-branch president Brandon Johnstone said the union welcomed a slower and more open vice-chancellor recruitment process.
"Any incoming vice-chancellor must come to our community with a willingness to join staff and student unions at the table and help to advance our mission for a healthier, more collaborative and accessible tertiary education sector," he said.
