Ndzinisa, along with fellow Swazi international attacking midfielder Felix Badernhost, was on a three-week trial at Bloemfontein Celtic last season but both players were turned away by then-coach Serame Letsoaka.
The 25-year-old recently scored four goals in their CAF Confederation Cup clash against Dikwena, in the second match of their group, as Swallows walked away 4-2 victors at Somhlolo Stadium.
According to the Mbabane-based outfit's general manager Sandile Zwane, Ndzinisa is likely to come back to South Africa, with Sundowns and Stars having raised their hands in interest in the Swazi striker.
"Our top striker Sabelo Ndzinisa, who scored those four goals against Platinum Stars, is wanted by everyone now," Zwane tells this website.
"Sundowns, yes, have shown interest and there's been an enquiry from Platinum Stars. These guys have been enquiring, and negotiations are ongoing but no deal is done as yet.
"I cannot specifically divulge more information at this stage, but no deal has been done so far."
Meanwhile, Badenhorst has since been snapped up by DR Congo giants AS Vita, whom he joined in August last year, shortly after his failed stint at Celtic.