The mill, in Dunaskin Street, Partick, is run by Premier Foods and mainly supplies flour to the Hovis bakery in Duke Street in the East End of the city.
But Premier Foods said it had too much capacity in its milling operations to justify keeping the site open.
The mill, near Partick Cross, is one of the smallest in the Premier Foods portfolio.
Bob Spooner, managing director of bread and the group supply chain director, said: "We recognise the impact our proposal will have on our employees.
"However, given excess capacity in our milling network, it is important we take the necessary steps to build a more sustainable milling business."
Premier Foods also said it was having to import wheat from the European Union after the UK harvest was the worst for 35 years.
Staff at the Partick mill may be given the chance to relocate to other Premier Foods sites, including the Duke Street bakery, a distribution depot at Eurocentral in Bellshill, Lanarkshire, and bakery ingredients division Fleming Howden at Newbridge, on the outskirts of Edinburgh.
Premier Foods said consultations with workers would start in the next few days and the mill could close by the end of March.