The Gallery of Modern Art, in Royal Exchange Square, is suffering from damaged stone work and is in need of repairs to the clock tower and ornamental weather vane.
Glasgow Life has applied to Glasgow City Council for permission to carry out the work, which they say will cost around £247,000.
The planning application, which has now been lodged with the local authority, states that the work will be carried out on the museum's iconic clock tower.
The tower sits on top of the main building giving the GoMA its distinctive shape.
The repairs are detailed as "stone cleaning and restoration, conservation to weather vane and clock faces, de-scaling masonry surface and indenting repairs to badly eroded masonry".
The tower's paint finish will also be removed and sandstone exposed.
A spokesman for Glasgow Life, an arms length body of the council, said the work is expected to take around six months to complete, subject to permission from Glasgow City Council.
He told the Evening Times: "We are working with a conservation architect to carry out restoration on the clock tower, to breathe new life into one of the city's most important landmarks."
Earlier this year we reported that one of the pillars at the front of the gallery had become stained with green algae, leading to outcry from councillors.
They claimed the visitor attraction had been left in a "disgusting state" when a leaking pipe caused water to run down the pillar creating a breeding ground for algae.
Glasgow Life said in January that the pipe, which one councillor claimed had been leaking for years, had been fixed but the pillar was yet to be cleaned.
They added that the algae has not caused any permanent damage to the building.
The GoMA is Scotland's most visited modern art gallery.
The city centre building is also home to the City Centre Library which also has a cafe.