The shipping magnate donated his treasures to the city during the Second World War and - despite living well into his nineties - died long before the Burrell Collection opened in Pollok Park in 1983.
It is one of the finest art collections ever acquired by a single individual.
It is a jewel in the cultural crown of our city.
But the building in which it's housed needs roof repairs, and the manner in which it's displayed is looking tired and needs refreshed.
The proposal is to start a £40million refurbishment to ensure the 8000-strong collection is shown at its very best.
But here's where it gets tricky.
The collection will have to close for up to four years while the work gets done and the curators at Glasgow Life want to send some of the Burrell's treasures on tour during the closure.
They argue that a high-profile tour - perhaps including a stop off at the Metropolitan Museum of Art in New York - would increase the reputation of the collection and encourage future visitors.
It might also raise donations to help pay for the work and allow other treasures to be loaned to Glasgow from around the world in return.
Visitor numbers at the Burrell have dipped to below 200,000 per year and the council and Glasgow Life believe publicity from a tour could see those numbers soar.
But Sir William Burrell was very specific when he gave his collection to the people of Glasgow.
He specified that the collection should be displayed in a countryside setting - hence Pollok Park - and that the pieces should not be sent on tour or loaned outside of the UK.
Other cities wanted the Burrell Collection but would not agree to those stipulations and were ruled out of the running, which eventually saw Glasgow triumph.
Can William Burrell's last will and testament be so easily set aside now when his wishes for the administration of his generous gift were so specific?
Well, that's what the Scottish Parliament has been asked to consider. A committee has been charged with looking at this issue and members toured the collection this week to hear the proposals.
The refurbishment needs to happen, the roof is leaking and if it's not fixed the collection will be damaged.
The council and, it's hoped, the lottery will be able to fund much of the refurbishment work but millions will still be needed from donations.
With higher standards of shipping and display for museum artefacts than existed in Burrell's day, his worries about his pieces being damaged could be a little out of date.
MSPs will now have to decide whether it's time Glasgow's treasures are displayed across the world.