The decision will be based on a report on the stadium’s progress by Ove Arup & Partners, which has been commissioned by Rugby World Cup chairman Leo Williams.
The Welsh Rugby Union is confident that Williams will give the go-ahead for the tournament’s opening game on 1 October.
A spokesman said: “I won’t be surprised if Mr Williams gives his endorsement this weekend. So far, he has not said yes but he has not said no. If he said no and we stage a successful game on 26 June, it would look a bit ridiculous.” A friendly against South Africa has been scheduled for 26 June in what will be a partially completed stadium.
Health and safety officers have agreed that 30 000 people can attend the match – the eventual capacity will be more than 70 000.
Laing is contractor and US firm O’Brien Kreitzberg is project manager on the scheme.