The Council's Environment Committee will discuss the proposals at a meeting next week.
It is understood the plans come after a review into cemeteries in the city.
Proposals for the planned improvements include:
- Structural rebuilding and repairs to sections of masonry walls
- Improvement works to drainage gullies
- Felling, pruning and planting of trees to repair previous storm damage
- Provision of new information boards and additional seating.
Commenting on the scheme, depute Environment Convener, Councillor Vari McDonald said: "These works will assist in maintaining safety at the site and to help improve this historic part of the city.
"The cemetery forms part of one of our important and popular open spaces in the city and I know that many people take the opportunity to walk there.
"I am sure these proposals will be widely welcomed."
(JP)