Van Rensburg was included in England's squad for the 2026 Nations Championship despite previously playing for the Junior Springboks and several South African franchises.
His stock has risen tremendously since he made the move overseas, first to the NEC Green Rockets in Japan and then to London Irish and now the Bristol Bears in the English Premiership.
The centre will qualify to play for England through five years of residency in the country, which triggers on 8 July 2026, meaning he will not be playing against the Springboks at Ellis Park this weekend but will most likely make his debut against Fiji the following weekend on 11 July.
Erasmus revealed the Springboks had seriously considered inviting Van Renseburg to join South Africa's Nations Championship squad due to his form and some depth issues at centre.
"If I tell the honest truth, we did have conversations with him. He was very keen to come," Erasmus said.
"Our CEO [Rian Oberholzer] asked me whether we were interested and I said yes, but we wanted to see where he'd fit into our selection plans.
"Then he asked whether we were going to try and cap him this year. I said no, I didn't think so.
"We then wanted to give him a chance in June because we were thin at centre with a lot of players away and we had the Barbarians game and the SA A game.
"But then our CEO reminded me that we'd already committed to World Rugby that we wouldn't go down that route. So we didn't pursue it."
Despite losing the centre to England, Erasmus wished Van Rensburg well and admitted he was happy the Boks would not have to face him on Saturday.
"I don't think people believe us when we say this, but when South Africans do well overseas, we're happy for them," Erasmus said.
"When they play against us, we want to beat them and tackle them backwards. But when a South African does well, we're happy.
"We're glad Bernard isn't playing against us [on Saturday] because we know him well. He's a tough man. That's why we considered him.
"But the fair thing was to give him the opportunity where he is."