Susan Deighan said the city would be seeking national funding to help secure the future of the historic landmarks on Glasgow Green, which have fallen into decline in modern times.
It is understood upwards of £20 million will be needed to bring them up to modern-day standards and realise the city’s ambitions.
Plans to consult the people of Glasgow on how the buildings, which date back to 1898, should be transformed will be set out this week.
Applications are expected to be made within the next months to secure funding for the buildings, which were closed down in 2018 due to their declining condition.
It is hoped the UK Government will support the project via the next phase of its £4.8 billion Levelling Up Fun, which closes for applications in July.
Glasgow has previously overhauled Kelvingrove Art Gallery and Museum, which reopened in 2006 after a three-year programme, while the Burrell Collection was closed for five years to allow the most recent work to be carried out.
More than 5000 people flocked to the Burrell Collection on Good Friday, its busiest day since reopening.
The People’s Palace was reopened for several months last year but had to be closed down again for emergency repairs after staff discovered that plaster was falling off its ceiling.
Ms Deighan has replaced Bridget McConnell as chief executive of Glasgow Life, which runs the city's museums and galleries on behalf of the council.Ms Deighan said: “Our next big project will be the People's People and the Winter Gardens.
"We are going to be announcing a consultation on their future this week.
"We will be building the findings into a funding application that are working on at the moment that we hope to put in towards the end of the summer."The council has already committed £2.9 million worth of investment (for restoration work) and we want to use that as a lever for other national funding.”
Ms Deighan said there was a need to bring the displays in the People's Palace up to date to reflect the city’s transformation in modern times.
She added: “The People’s Palace is at the heart of Glasgow Green and tells the story of the city, its culture and its people. As a child of Glasgow, it's very important to me personally.
"Anybody who has lived or grown up in the city will have enormous emotional ties to the People’s Palace.
“Heritage isn’t just about built heritage. The People’s Palace tells the stories of Glasgow, but we have to ensure that those stories are contemporary and that they reflect where Glasgow is today.”
"From a cultural perspective in Glasgow, it’s a project that we really want to prioritise and the next one we’ve really got in our sights.
"We’ve always been committed to the People’s Palace – we’ve said that on many occasions. I would hope there’s been no question marks over its future.
"But this next phase will hopefully start to demonstrate that we mean what we say and that we’re working on it as our next priority.”