The park's trust board has sought resource consent from the Auckland Council to remove the two magnolias. Its application was publicly notified on Monday. The council says if it gets submissions then a hearing was likely in November.
The board's heritage consultant, Adina Brown, said in a report that the magnolias were planted in the middle and late 20th century.
They were not part of the original landscape plan when the statue and fountain were unveiled in 1906.
The Campbell monument is of "exceptional historic heritage value", but not the trees.
"The magnolia trees themselves are of little/no historical value because they are not associated with Sir John Logan Campbell or any other notable historical figure.
"They were not part of any of the historical events that have taken place in the park, such as the unveiling of the statue or commemoration of ... Campbell's death. They are not known to have a strong public association."
"The tree removal will significantly improve the visual dominance of the Logan Campbell fountain and statue both within the park and when viewed from surrounding footpaths and roads, as was the original design intent."
The growth of the trees had "degraded" the landmark status of the monument and their removal would recreate the grand nature of the entrance.
"The original design was intended to be largely free of trees, consisting of a grassed lawn; however, by the 1940s perimeter planting , possibly including the scheduled magnolia trees, appears to have taken place, giving it more of an arboretum character."
Pohutukawa near the monument and puriri trees in Puriri Drive would be retained, Brown said.
Mark White, the council's manager of central resource consenting, said the council had no view at this stage on the request to fell the trees.
"A recommendation will be made following a comprehensive review of all the information lodged as part of the application and any submissions following the notification process."