Mr Webb said the member of the public who had alerted him to the tree believed the only people who could benefit from it dying were residents of Maxwells Rd or Andrew Place.
"There is an elevated ridge up there and the person who called us believed the tree was blocking someone's view.
"They are probably right.
"However, the problem is unless someone saw this happening or knows who did it, we cannot do anything about it."
He said damaging the tree was a criminal offence and the council was keen to follow it up.
"At this stage we do not know what will happen to the tree. It could die completely but we are hoping it will survive and only a section of it dies. It is just a matter of waiting and hoping for the best. It all depends on how good a job the person did poisoning it."