The 3,500-seater auditorium is part of a £500m redevelopment project to transform the city centre.
Swansea council has advertised for an operator to run the facility on the former St David's shopping centre site.
Officials hope a new arena will attract touring live shows from hit programmes such as Strictly Come Dancing and X Factor.
Swansea council said survey work at the site had been carried out and an outline planning application was due to be submitted in March.
Other ideas for the former St David's complex include a café and restaurant quarter as well as a cinema.
The proposals were announced in January alongside a scheme to transform the Civic Centre site into apartments, an aquarium as well as an aquatic sciences research centre.
It is hoped the two projects would create 1,700 permanent jobs in the future.

Zoo staff are helping the rare sea turtle to recovery after it got a little bit lost last year.
Menai is an Olive Ridley turtle, which are usually found in much warmer waters around Mexico.
It's thought that Menai was knocked off course for thousands of miles by strong currents.
Vets are giving her lots of checks to make sure she is healthy and they say she is recovering well.

The memorial and museum tweeted that the gas chamber was "not a stage" but was a place for mournful silence.
Republican Clay Higgins said in the video that the horrors of the WW2 death camps were the reason why the US military should be "invincible".
Some 1.1 million people, mainly Jews, died at the Nazi-occupied Poland camp.
Mr Higgins made a five-minute video showing him in different parts of the museum talking about the atrocities in the death camp.
At one point, he goes inside a gas chamber and explains how the victims were gassed.
"This is why Homeland Security must be squared away, why our military must be invincible," he says.
But the museum responded that it was inappropriate to speak inside the gas chambers.
"Everyone has the right to personal reflections. However, inside a former gas chamber, there should be mournful silence. It's not a stage," it tweeted on Tuesday.
Later it posted a picture of the entrance to the building showing a plaque asking for silence.
The Louisiana congressman has not yet responded to the criticism. His offices were closed for the Fourth of July holiday.
However, the video was not being displayed on his website and social media users suggested it had been removed.
The Anti-Defamation League, an American-Jewish anti-discrimination organisation, said the video was "incredibly disrespectful to the hallowed ground" of the memorial and museum.
Some Twitter users reacted with fury.

At one point the drone was just 30m (100ft) from the plane which had to take evasive action to avoid a collision, officials said.
A navy spokesman accused the Iranians of behaving in an "unsafe and unprofessional" manner.
Tensions between the countries are high with the Gulf a potential flashpoint.
US Naval Forces Central Command spokesman Commander Bill Urban said the incident happened in international air space as an F/A-18E Super Hornet was preparing to land on the USS Nimitz.
Despite radio warnings to stay clear of the carrier, the drone carried out "unsafe and unprofessional" altitude changes near the jet, he said.
"The dangerous manoeuvre by the QOM-1 [drone] in the known vicinity of fixed-wing flight operations and at coincident altitude with operating aircraft created a collision hazard and is not in keeping with international maritime customs and laws," Cdr Urban said.
The incident is the latest in a series of close encounters in the Gulf between US and Iranian forces.
In July, a US Navy ship fired warning shots at an Iranian Revolutionary Guard vessel after it came within 140m (450ft) and ignored radio calls.
In January, a US destroyer fired three warning shots when Iranian fast-attack vessels approached at high speed in the Strait of Hormuz.
A planned indoor arena for Swansea has come a step closer as council bosses begin looking for a firm to run it.
[NEXT_CONCEPT]
Menai the turtle was found washed up on a beach in Wales in November, and was rescued by wildlife experts in Anglesey.
[NEXT_CONCEPT]
Officials at Auschwitz have criticised a US congressman for making and voicing a video inside a gas chamber at the former Nazi death camp.
[NEXT_CONCEPT]
An Iranian drone has flown dangerously close to a US fighter jet as it was about to land on a carrier in the Gulf, the US Navy says.