The Museum of Childhood recently underwent a refurbishment

Council leader Adam McVey said a different regime for visitors and locals was one possible move which could come from a review of the city’s cultural services as part of budget cuts aimed at saving £150 million by 2023.

And he revealed the council was also looking at handing the management of its museums and galleries to an expanded Edinburgh Leisure, which already runs the city’s sports centres and swimming pools.

“We need to look at whether we keep cultural services directly run by the council or whether we look at a model that has a way of pooling assets.”

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He said the Glasgow Life trust, which runs sport, leisure and culture in Glasgow, seemed to be a model which worked well.

Budget proposals published by the Capital’s SNP-Labour coalition suggest “consolidating” venues like the Museum of Childhood, Museum of Edinburgh, Writers’ Museum, People’s Story and City Art Centre and creating a new museum and gallery.

But Cllr McVey played down suggestions of a new building and hinted the move was more likely to involve moving at least some elements from other venues into the City Art Centre.

He said: “The City Art Centre is a massive building which is heavily under-used. We need to make much more of it if we are going to have it as a city asset, making sure people know it’s there and capturing people’s interest. It is competing with some fantastic national assets. It needs to work much harder for the city.”

He said merging the museums into a single building was “probably not feasible”.

And he said: “We do not have a hit list of buildings we are trying to close or tamper with. But we are looking at whether we have the right buildings displaying the right things in the right place.”

The budget proposals show a planned saving of £500,000 on culture by 2023.

Visitor numbers at the city’s museums increased after the council reversed a cut in opening hours last year.

Cllr McVey said: “I think the museums are working quite well but we can do a lot more in terms of a better offering to tell the story we have to tell and getting our fantastic art and exhibits on display for people to see. We must not rest on our laurels.”

City Centre Tory councillor Joanna Mowat said she was not against the changes proposed. “A lot of tourists are perfectly used to paying for museums. I have to pay when I go to Paris.”

She said her party had previously argued for a trust like Glasgow Life.

And she said: “It has always been known we need to look at our buildings but we never seem to push forward with any urgency. How much faith can we have that this is not just a fantasy budget?”

Green councillor Gavin Corbett said: “I’m not opposed to looking at different options for hosting the city’s museums and for how buildings are used.”