The proposed space, part of the Central Square scheme near Cardiff Central rail station, would see the St David's House building on Wood Street demolished.
Three fully-let office buildings and a transport interchange, including office and residential units, have already been given the go-ahead.
Cardiff council's cabinet discussed the public space plan on Thursday.
Councillors gave the authority permission to dispose of leasehold interest in land north of Wood Street to enable the 270,000 sq ft (25,083 sq m) office block and square to be built.
The proposal will also include a new office development, which could accommodate 3,000 jobs, on the site of the old Western Mail and Echo building on Park Street.
The new BBC Wales Cymru headquarters, at the heart of the new Central Square development, is already under construction while a new transport hub has been given full planning permission.
Council leader Phil Bale said: "As anyone can see, the transformation on the south side of Wood Street facing the railway station is well under way with the BBC Wales HQ and No 2 Central Square beginning to take shape alongside No 1 Central Square which has been open for over a year.
"Now there are some really exciting plans coming forward for the north side of Wood Street on the old Western Mail and Echo site, which has been empty for several years, and on the St David's House site which fronts Wood Street."
Councillor Elizabeth Clark, leader of the Liberal Democrat opposition on Cardiff council, said: "The Labour run Cardiff council need to provide more detail on the use of the public square.
"For example, how will pedestrians, cyclists and the proposed metro be accommodated? It's important to get all this right."

Last summer, he pulled out of the Stormont Executive when Peter Robinson was away, initially wrong footing the DUP as it tried to respond to allegations that Provisional IRA members were involved in the murder of former IRA man Kevin McGuigan.
When Peter Robinson returned, he had to engage in some unpopular tactics, such as the DUP's rolling ministerial resignations, to buy time for Stormont.
However, his successor Arlene Foster reaped the dividend in the assembly election, by maintaining her party's dominance.
The DUP has more than a two to one advantage over the Ulster Unionists.
Mr Nesbitt has undoubtedly lost some of the momentum built up by last year's Westminster election.
But, he hasn't abandoned his sense of timing.
Thursday's inaugural meeting of the assembly looked like it would be all about protocol and procedure.
Mrs Foster was itching to get back to the DUP's stand at the Balmoral Agricultural Show.
The TUV leader Jim Allister spiced up proceedings by launching an attack on the new principal deputy speaker, Sinn F??in's Caitr??ona Ruane.
Then, at 15:10 BST, the story changed.
Mike Nesbitt's announcement that, so far as he is concerned, the programme for government negotiations are over surprised MLAs beyond his own party ranks.
His rallying call of "let battle commence" ensures the political game at Stormont will change.
Business in the assembly could start looking a little more like Westminster, although for historic reasons it's hard to imagine the DUP and Sinn F??in sitting on the same side of the chamber facing their opponents.
The SDLP insist the Ulster Unionist decision does not put them under extra pressure.
They will continue to negotiate about the executive's future policy.
But, with Mike Nesbitt enjoying the extra speaking rights and other privileges accorded to an official opposition, SDLP politicians will inevitably need to consider whether they will pale by comparison.
Not only do they need to consider the impact of having the UUP outside the executive, but also the more pugnacious role smaller parties like People Before Profit and the Greens might play in the future.
Sinn F??in reckons Mike Nesbitt has repudiated the principles of the Good Friday Agreement that David Trimble signed up to 1998.
The DUP is dismissive, insisting Mr Nesbitt is "running into opposition having lost the election".
DUP sources claim the Ulster Unionists were so semi-detached when they were in the power-sharing coalition that this latest move will change little.
That said, Arlene Foster herself told me on Monday that "perhaps it would be more honest" if those who previously opposed the executive from the inside did so instead from the outside.
Mike Nesbitt has taken her at her word and we now have five years to work out if his gambit pays off.
A new public square has been proposed as part of plans for the next phase of Cardiff city centre's regeneration.
[NEXT_CONCEPT]
As a former TV presenter, Mike Nesbitt has a penchant for grabbing a headline.