Funding for felling the two redwoods has been set aside and it is intended to call tenders later this year.
Ms Hayes said the work would take several weeks with specialist equipment needed to bring the 45m high trees safely to the ground.
The two trees were part of the 1878 planting of redwoods in the cemetery and adjacent Queen Elizabeth Park by pioneer W.W.McCardle.
Times-Age gardening expert Gareth Winter said in North America sequoiadendron giganteum are known as Californian Big Trees and can be expected to live well beyond 1000 years.
One specimen named General Sherman after American Civil War general William Tecumseh Sherman is, by volume, the largest living single-stemmed tree on earth with a 31m circumference but is not the world's tallest tree.
An even bigger redwood, by volume, was felled in 1940.
There is some debate over the world's tallest tree but most experts bestow that honour on a coast redwood (sequoia sempervirens) named Hyperion which is found in Northern California and measures 115.61m in height.
Mr Winter said redwoods were only really discovered in the wild during the Californian gold rush in the mid 1800s and became "quite fashionable" with plantings in many places throughout the English-speaking world.
The relatively short life of the two Masterton redwoods which are to be felled was probably due to two main factors, he said.
"Our climate is not quite as moist as their natural habitat and the soil conditions didn't suit them.
"Many of the cemetery and park trees have been planted on top of old river beds and that accounts for the reason why a lot of the trees there are very shallow rooted," he said.
Mr winter said an issue facing the council was that as the redwoods die off and need replacing it would need to be with varieties that grow to a similar shape otherwise the landscape balance of the park would be altered.
