Since it was completed in 2016 the concrete behemoth has divided opinion, with some viewing it as a new landmark for the city and others a blight on the landscape.
Proposals to liven up the grey facade have included allowing local artists to paint murals on it, and lighting it up with artful illuminations.
But now a local architect firm thinks the 118m tower would be the ideal location for a climbing wall, according to newspaper Neue Zürcher Zeitung.
The idea is technically achievable and should cost around 10,000 francs to install, the IG Zürinordwand firm’s board member Robert Fischer, himself a climber, told the paper.
The idea isn’t new. Industrial buildings in Vienna sport climbing routes, while a hotel in Reno, in the US, has a climbing wall up one side.
With its 118m height, the Swissmill silo could become the tallest urban climbing route in the world, said the paper.
In the coming days IG Zürinordwand intends to send an open letter to Swissmill’s owners to suggest the idea, said the paper.
Switzerland already holds the record for the tallest non-urban artificial climbing route in the world, which stretches for 160m up the Luzzone dam in the canton of Ticino.
The Swissmill silo – also known as the Kornhaus – opened in its current form in 2016 after three years of construction work to extend a previous 40m silo on the site.
It is the second highest building in Zurich after the Prime Tower, which stands at 126m.
Currently the tallest building in Switzerland is the 178m Roche Tower in Basel.
The pharmaceutical company is set to break its own record by constructing a 205m office block, designed by Herzog & de Meuron, due to open in 2021.
But Switzerland’s tallest buildings are dwarfed by the country’s huge dams, the highest of which is the Grande-Dixence in the Valais, at 285m.