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Her second five-year term is due to run out in August next year.
The university has not yet indicated what timelines it will be working to for filling the position, but when Prof Hayne was reappointed in 2016, the announcement was made in March of that year.
A university spokeswoman said no recruitment plans, processes or timeframes were in place yet.
Chancellor Royden Somerville said he would not be indicating publicly what was happening with the process at the moment.
It is rare for a vice-chancellor to go beyond two five-year terms.
Sir Robin Irvine (1973-93) is the only example at Otago since 1948, when vice-chancellors took on their current role at the university, effectively becoming its full-time chief executive as well as academic and administrative head.
Prof Hayne, the first female vice-chancellor of the university, assumed the role in 2011, having previously been the research and enterprise deputy vice-chancellor and head of the psychology department.
She has been employed by the University of Otago since 1992.