The statue, which stood at the front of the R&I Bank building on Barrack Street from 1979 before being relocated to Perth Town Hall in 2003, has been in storage since 2012.
The council's decision last week to find a new home comes just weeks after Stirling Mayor Giovanni Italiano approached Lord Mayor Lisa Scaffidi about the sculpture of Western Australia's first governor being relocated to Stirling Civic Gardens.
A motion at the council meeting to place it at either the Perth Town Hall or Stirling Gardens was replaced by Ms Scaffidi with one suggesting the new Perth City Library, which was passed unanimously.
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READ NOWMs Scaffidi said historical records showed Governor Stirling had little connection to the original suggestions.
"It's important to ensure the placement of the statue reflects the historical links Governor Stirling had with an area to appropriately honour the role he played as the city's founding father," she said.
Ms Scaffidi said reinstating the statue at the entrance to the new library in time for its opening was "ideal" but also suggested the Hay Street footpath near the new piazza was also a suitable candidate.
She said Cr Italiano approached her in June about Stirling reclaiming the statue and she responded with a letter.
"I wrote a letter saying "thanks but no thanks", she said.
Ms Scaffidi said she would open discussions with the Perth Diocesan Trustees about the possibility of the Cathedral Plaza being a suitable location for the statue.
"Governor Stirling temporarily operated in the vicinity," she said.
When the Express asked if the activity was prompted by Cr Italiano's inquiries, Ms Scaffidi said it was important time was taken to find the right location to reflect on the important role Governor Stirling played as the city's founding father.