Environmental affairs spokesperson Mandla Mathebula said SA National Parks (SANParks) and the departments of environmental affairs and public works were discussing the logistics.
The fence is to be re-erected following a surge in rhino poaching in the Kruger National Park.
"Their meeting is taking place," he said. "I am unable to give further details."
Mathebula said there was no threat to the Great Limpopo Transfrontier Park, which incorporated national parks in South Africa, Mozambique, and Zimbabwe.
"The transfrontier park will remain intact," he said.
"This does not change the transfrontier park.
The first elephants were translocated from the Kruger to the Mozambican side of the transfrontier park in October 2001.
Former president Nelson Mandela joked at the time that the elephants were lobola for his Mozambican wife Graca Machel.
The release of the elephants was supposed to signal the start of a fenceless mega park, incorporating the Limpopo National Park in Mozambique, the Kruger, and Gonarezhou National Park in Zimbabwe.
But a spike in rhino poaching has caused wildlife officials to call for the fence to be re-erected.
Environmental Affairs Minister Edna Molewa told the National Press Club in Pretoria on Sunday that an additional 150 rangers would be deployed to the Kruger this year to combat rhino poaching.
She said government would add them to the existing 500 rangers currently employed in the park.
Two poachers have been killed and another two have been arrested in connection with rhino poaching in the Kruger this year.
In 2011, 448 rhino were killed in South Africa.
Another 11 have been killed in the country this year so far.
One of the department's plans included re-erecting the 150km stretch of fence along the border with Mozambique.
Molewa said 232 people had been arrested for rhino poaching.
SANparks chief executive David Mabunda, who was also at the briefing, said the fence, if approved, would cost an estimated R250m to build.
"We still have a fence or what used to be a fence. That part of the fence is in a bad state of repair."
The proposed fence would be electrified but would not be lethal, and serve more as an early warning system, Mabunda said.
Most of those caught poaching were Mozambican nationals with some South Africans involved. Very few Zimbabweans were involved in poaching in the Kruger.
Mozambicans living across the border of the park were extremely poor and could therefore be enticed by organised crime.
"We need an appropriate organised response," he said.
South Africa has around 22 000 rhino, which is about 80% of the world's rhino population.
The country's rhino population, 22% of which is in private hands, is growing.
However, if poaching levels continued to climb, from 2015 South Africa could see a fall in its rhino population, Mabunda warned.
In the 1960s and 1970s, Africa's rhino population was being exterminated at the rate of about 8 000 animals a year.
Rhino horn rhino is valued for dagger handles in Yemen, while in China and Vietnam it is prized in traditional medicine to treat fevers.
SANparks spokesperson Reynold Thakhuli said on Monday that most of the rhino poaching was being done in the south of the park near camps such as Lower Sabie and Pretoriuskop.
The fence, he said, was likely to cover only certain areas.
Further details would be released once the meeting on Monday had been concluded.