For decades, the water in New York’s rivers have been considered too filthy for swimming.

But the sight of people splashing about in front of the Manhattan skyline could again become a part of city life, following the launch of a project to revive swimming in the East River.

The city is inviting proposals for a “self-filtering” pool off lower Manhattan between Brooklyn and Manhattan bridges that would enable the public to safely swim in the middle of the city.

If the plan goes ahead, it would become one of America’s first urban river swimming facilities. It would also bring back a tradition that dates back to the late 19th century, when the East River was dotted with free public floating baths, until pollution led to their demise in the 1930s.

The New York City Economic Development Corporation (NYCEDC) has put out a call for people “interested in developing, installing, and operating a self-filtering swim facility to be located in the East River off lower Manhattan”.

Among the organisations planning to submit a proposal is not-for-profit +Pool, which has created a design for what it believes is the world’s first water-filtering floating pool.

The concept was first conceived nearly nine years ago by a group of artists and architects. The plus-sign shaped, 9,000 sq ft design has four separate sections for sports, relaxing, laps and children that can also be combined to form an Olympic length pool.

Its chlorine-free filter system pushes river water through the walls of the pool, acting as a “giant strainer” that removes bacteria, odours and contaminants without removing the water’s salt content, and pushes clean water out. The organisation estimates the system can clean over 600,000 gallons of water per day.

Kara Meyer, the managing director of +Pool, said: “Swimming in natural water is a totally different experience. To be able to do it in such an iconic city like New York city is life-changing.”

+Pool has been working on this idea and advocating for it since 2010 – gaining widespread publicity in the process. Last month NYCEDC put out a “request for expressions of interest”, inviting interested parties to come forward with proposals by 1 November . Proposals have to demonstrate how the project would provide long-term access to the public to swim in the river, benefit the local community, how the filtration system would work and how they will finance construction, installation and running costs without funding from NYCEDC or the city.

While the request marks a significant step in the project, there are still many hurdles to overcome. The party that is chosen for the project will then enter into a “predevelopment agreement” when they will need to present their design and get all the necessary federal, state and city approvals and permits before construction can start.

Although the Clean Water Act has led to a vast improvement in the water quality of New York Harbour – “no one in our lifetime has seen it as clean and healthy”, according to the 2018 Harbour Water Quality Report, and there has been an increase in whale sightings – it still has an image problem.

“There’s a huge negative public perception on the waters around New York. There have been for quite some time. So a lot of the work that we’ve been doing as an educational organisation is just to share that that’s not necessarily true,” added Meyer.

According to early estimates, +Pool would cost $20m to create, funds which it plans to raise privately, and one year to build. Last week it launched a light installation in the river to indicate cleanliness that links to an online water quality “dashboard”.

The project reflects New Yorkers’ changing relationship with its waterways in recent years. The city has moved to improve access including waterfront parks and launched a citywide ferry service.

Allison Dees, the NYCEDC assistant vice-president, said: “We are excited to be examining the feasibility of a floating swimming facility in New York’s harbour, as it will promote a sustainable approach to enjoying our rivers and further activate our waterfront for the enjoyment of New Yorkers in a creative way.”