Ndzinisa, who was recently linked with a move to AmaZulu, reportedly arrived in South Africa last week to train with Matsatsantsa under the watchful eye of coach Eric Tinkler.
The Sihlangu Semnikati forward, who also had a trial at Bloemfontein Celtic over a year ago, raised his continental profile when he plundered four goals in a CAF Confederation Cup win over Platinum Stars at Somhlolo Stadium in May.
According to reports in Swaziland, Ndzinisa - the top goalscorer in the Swazi Premier League last season with 19 goals - is expected to spend a week with United in a bid to win over Tinkler.
"Ndzinisa is in South Africa. He left last week Thursday to train with SuperSport United," says a source close to Swallows.
"He had two other options in Belgium and AmaZulu but decided to try his luck with SuperSport United."
Swallows boss Victor Gamedze confirmed that there is interest in Ndzinisa from a South African team but he refused to provide details.