Site sources say contractor Laing and project manager O'Brien Kreitzberg want the game to be cancelled to ensure that they can finish the stadium for October's rugby World Cup.
But the Welsh Rugby Union has insisted that the stadium will be open for the South Africa match, albeit with a reduced, 45 000 capacity.
Stadium chairman Glanmor Griffiths said this week: "The stadium will be ready for the South Africa game. Everything is on programme to deliver it for 26 June." He said he would be replying to a letter from the South African rugby union as soon as possible.
But this week, the South Africans were still in the dark. Speaking from Johannesburg, South African rugby union games controller Steven Roos said: "I have written to the Welsh Rugby Union to see if the fixture is still on, but I haven't heard anything.
"I've asked the question because we need to plan and organise flight bookings and hotels. From London, our players will be leaving directly for a tournament in Australia and New Zealand, so there is a lot of organising to do." Laing and O'Brien Kreitzberg both declined to comment on the South Africa fixture, but the team on site is understood to want to concentrate its efforts on the areas of the stadium that are less well advanced.
But, to get a 45 000 capacity by June, it would have to complete the more advanced areas of the stadium. The north stand and parts of the east and west stand could be ready for a June opening, but the south stand would be far from finished.
Laing, which has already lost £20m on the project, will face severe penalties if the stadium misses the World Cup deadline.
It does stand to gain in a small way if the South Africa game goes ahead, as it will take a portion of the gate receipts.