Foreign ministry spokesperson Kimiebi Imomotimi Ebienfa told the BBC that the issue would be discussed between the two governments "at the highest levels".
Acting High Commissioner to South Africa Alexander Ajayi said on local television on Tuesday that the government had begun documenting businesses and properties left behind by Nigerians.
One Nigerian trader waiting to be repatriated told the BBC he had lived in South Africa for nearly a decade and had abandoned his business and home because he feared for his safety.
Oghodero Erejor Wilson, 32, said he was losing "everything because of fear".
"I left everything in my house including clothes."
He is among hundreds of Nigerians still waiting to be evacuated from South Africa. More than 600 Nigerians have already been repatriated in recent weeks.
The South African authorities say those who have been flown home were in the country illegally - though this is disputed by Nigeria.
About 25,000 nationals of other African countries have left South Africa following a wave of protests in recent weeks by groups demanding that the government does more to curb illegal migration.
Some anti-migrant groups had given undocumented foreigners a deadline of 30 June to leave the country and organised marches attended by thousands of people on Tuesday. These were largely peaceful but there were isolated incidents of violence against foreigners.
The South African police say that about 900 people were arrested, mostly for immigration-related offences and looting.
The BBC has asked South Africa's government for comment on Nigeria's compensation demand.
Getty Images South Africans holding sticks to protest illegal migration to their countryGetty Images
Tuesday's marches were largely peaceful but there were isolated incidents of violence
Nigeria's acting high commissioner said he had asked all of those who had left South Africa "to document very accurately those things they were leaving behind in terms of businesses, in terms of even cars, movable and immovable properties".
Foreign ministry spokesperson Ebienfa told the BBC that all claims would be verified before any formal request was made.
"We have not severed ties with South Africa, we are still engaging them at the highest level, we will sort those details using our usual diplomatic channels," he said.
Wilson, the trader, said he had run a clothing business in the South African city of Centurion in Gauteng province for several years.
But he said he had now closed his shop and fled to stay near the Nigeria High Commission in South Africa's capital, Pretoria.
Scheduled to leave on the next repatriation flight to Nigeria on Friday, he estimates the goods left in his shop are worth more than 16,000 rand ($975; £735).
Wilson said his residency documents had expired in 2021 and he had been unable to renew them.
He said he was not very hopeful about the prospect of getting compensation.
"If South Africa government can compensate it, it will be nice, but I know they won't," he said.