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3 December 2014 Last updated at 14:08 GMT
The bridge, for pedestrians only, would cost Â£175m to build, making it the world's most expensive footbridge.
Lambeth and Westminster councils, who are in charge of new buildings in areas of London, have both said the bridge can go ahead.
But some people aren't happy with the idea, saying it could spoil views on the riverside, including St Paul's Cathedral.
London's Mayor, Boris Johnson, will have the final say over whether the bridge can be built as planned.
Check out Ricky's report for more on this story.

Leah Kerry was found unconscious at about 04:50 BST on Saturday at Bakers Park in Newton Abbot, Devon.
Jacob Khanlarian from Newton Abbot, was charged with two counts of intent to supply a class A drug and one of intent to supply a class B substance.
The 20-year-old entered no plea and was remanded in custody by Plymouth magistrates.
He will appear before Exeter Crown Court on 10 August.
More on the drug-related death and other Devon news
It is believed Leah, who was not from the area, suffered an adverse reaction from the substance. She died in Torbay Hospital.
Two other girls believed to have taken the same substance were also taken to hospital over the weekend as a precaution, but have since been released.
Det Supt Ken Lamont said: "With NPS (New Psychoactive Substances) no-one knows what's in them and that's why they are so dangerous.
"Time and time again we hear of people paying the ultimate price for this.
"It's not worth experimenting with your life."
Last year Totnes teenager Nathan Wood died after after taking the psychoactive drug N-Bomb.
Police called on parents to "speak to your children about the dangers of drugs and legal highs".

Reports suggest Chinese buyers are acquiring the clothing retailer, which started in London in the 1850s.
Its illustrious fans have included the Queen Mother, Margaret Thatcher and actors such as Cary Grant.
But after the British firm was saved from administration in 2012, it has mainly focused on China and last year saw its UK sales fall 16%.
Hong Kong-based YGM Trading, which bought it for £15m four years ago, said Aquascutum is due to be sold in March 2017 to two buyers.
The unnamed acquirers have made a $5m down payment for exclusive rights to the deal, YGM said in its annual report this week.
Chinese textile firm Shandong Ruyi Group is understood to be one of the buyers, according to Bloomberg.
Aquascutum started as a Mayfair tailors in 1851, rising to prominence after its founder, John Emary, patented the first waterproof textile.
Its trench coats were worn by British soldiers during the First World War, while in 1953 its wyncol fabric - designed to withstand 100 mph winds - was used by explorer Edmund Hillary in the first confirmed ascent of Mount Everest.
The coats were also a regular feature on the silver screen, with Sean Connery wearing one in Another Time, Another Place in 1958 and Sophia Loren in The Key.
However, the retailer has struggled in recent years, closing its Nottinghamshire factory in 2012 and then falling into administration.
Under YGM's ownership, the company's primary focus has been China, with 135 of its 146 outlets located in mainland China, Hong Kong, Macau and Taiwan.
Last year it closed 14 stores in China amid declining sales, but opened one in Europe.
In the UK, its three remaining standalone stores are in Westfield London, Great Marlborough Street and Jermyn Street.

Daniel Timbers, 29, and Barry Joy, 56, were working at Harford Attachments in Spar Road when they were killed, shortly after 09:00 BST on Monday.
The men are believed to have been working in a paint-spraying area.
Their bodies were removed from the site on Tuesday afternoon.
A forensic search has been carried out at the company, which makes buckets for diggers.
Det Ch Insp Paul Durham said "significant progress" had been made with forensic inquiries and obtaining witness statements.
"Evidence gathered so far suggests there has been a flashover explosion, which occurs when you have a build-up of toxic fumes," he said.
"This, combined with some sort of ignition, has caused a fire-ball effect."
The Health and Safety Executive said its inspectors and electrical safety experts would be gathering evidence.
A huge garden bridge over the River Thames in London is a step closer after plans were approved by local council officials.
[NEXT_CONCEPT]
A man has been charged following the death of 15-year-old girl suspected of taking drugs.
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Aquascutum, whose luxury raincoats have been worn by royalty and film stars, is being sold for $120m (£97m).
[NEXT_CONCEPT]
Two men killed in an explosion at a factory in Norwich died from the "effects of fire and inhalation of fumes of combustion", post-mortem examinations have found.