National Assembly Speaker Baleka Mbete says an external service provider has been appointed to look into the feasibility of moving Parliament to Pretoria.
Former president Jacob Zuma first made the suggestion, in his 2016 State of the Nation Address, to move the national legislature to the country's capital.
This was in order to cut costs, he argued.
During Parliament's budget debate on Tuesday, Mbete announced that Pamoja PTY LTD had been appointed to conduct a "six-month socio-economic and impact study" on the proposal, commencing this month.
"This [is] a matter that we will hand over to the sixth Parliament," Mbete said in her speech.
That means the results of the study and its feasibility or non-feasibility will be looked at only after the 2019 general elections by the newly-elected Parliament.
Zuma said, in his SONA two years ago, that a "big expenditure item that we would like to persuade Parliament to consider is the maintenance of two capitals, Pretoria as the administrative one and Cape Town as the legislative capital".
It was costly for Cabinet to spread its work over the two capitals, he said at the time.
In February 2016, Congress of SA Trade Unions (Cosatu) and Nomura economist Peter Attard Montalto said moving South Africa's Parliament from Cape Town to Pretoria would cost R7bn, but could bring savings of around R500m to R750m a year.
The proposed move, however, also received its fair share of criticism.
Cosatu at the time said it was concerned for the future of its members in Cape Town, saying the proposal might sound good in principle, "but it cannot simply be based upon saving ministerial costs", Fin24 reported.
"Moving Parliament would mean uprooting 1 400 parliamentary staff and their families from their homes," the union federation said in a statement. "The estimated cost of moving Parliament is R7bn, and we don't know where such money would come from.
"While we fully support cost cutting, it must not come at the expense of workers and their families."
Other critics included Montalto, who said it would cost too much to build a new Parliament, and Cape Town Mayor Patricia de Lille, who said the ruling party should look at first cutting the size of the Cabinet before anything else.
During question sessions, Zuma said there were spare government buildings not being used in Pretoria that could serve as a potential new home for Parliament.
It was not clear what would become of Cape Town's parliamentary buildings if the move is approved within the next few years.