The council has confirmed four of the trees have died, including a kauri dedicated to poet Charles Brasch planted in 1976 and a mountain beech dedicated to geography lecturer Robin Law planted in 2004.
The council has issued an apology to friends and associates of the two men, and to the university.
ORC chief executive Sarah Gardner said the council hoped to replace the trees with others "of the same size and species".
Using wood from the two trees for a feature or sculpture would be another way to help contribute to the university's vision of a "contemplative and shady garden", she said.
Ms Gardner said the ORC wanted to acknowledge the significance of both the memorials, and the work of Brasch and Dr Law.
Brasch had a strong connection to the University of Otago, helping to found the Burns Arts Fellowship, 60 years ago.
He was also the founder and first editor of the Landfall arts and literary journal, which began in 1947.
Dr Law, who specialised in feminist geography, joined the university in 1994, and died in 2003.
The university had been in contact with the ORC.
"We treasure our memorial trees. We want to emphasise the importance of them to our university, families and colleagues," a university spokeswoman said.
"So we are working with the Otago Regional Council to ensure this is resolved in an appropriate and sensitive way."