Plans for the city's LC leisure centre would see a sports climbing wall installed on the outside of the building.
But it has been also been designed to be a giant mural, as part of a series of pieces brightening up the regenerated waterfront.
The Â£300,000 project is a one of five new public exhibits being put forward.
If given the go-ahead by council planners, the permanent artworks are likely to be installed next year along Quay Parade and Oystermouth Road - a route into the city centre used by tens of thousands of motorists, cyclists and pedestrians every day.
As well as being a piece of art, the climbing wall would be used as a resource for climbers of all abilities, with instructors on hand to help.
It would be folded up in the evening to ensure nobody could climb it unsupervised.
Other proposed exhibits include:
Councillor Robert Francis-Davies, cabinet member for enterprise, development and regeneration, said the council wanted visitors, commuters and residents to "receive a welcome that's both memorable and unique to us".
"Public art can play an important role in city centre regeneration," he said.
"It helps enhance the character and uniqueness of a city, emphasises key locations, gives a sense of place, encourages exploration and often generates long-lasting and memorable experiences that will encourage people to return in future."
Climbers could soon scale the heights of a Swansea landmark - and become part of public art in the process.