Any safety agreement that would allow the club to occupy 9,000 currently empty temporary seats would depend on it.
Unions circulated a letter calling on the brands to commit to a legally binding safety agreement by May 15.
The factory safety agreement calls for independent, rigorous factory safety inspections with public reports and mandatory repairs and renovations underwritten by Western retailers.
H&M did not have clothes made at the site and was the first company to sign a safety agreement for Bangladeshi factories after the disaster.
Now, more than 50 brands have signed up to a legally binding building safety agreement backed by the international trade union IndustriALL and the Bangladeshi government.
But the company, and Gap, have refused to sign a legally binding safety agreement known as accord on fire and building safety in Bangladesh, that has the support of other retailers including H&M, Primark and Tesco.
River Island and Matalan join more than 80 brands from around the world, which have now signed up to the legally binding building safety agreement, pledging to contribute up to $500,000£325,00000) a year towards independent factory inspections and fire safety measures.
Campaigners are urging companies to sign up instead to the Bangladesh Fire and Building Safety Agreement (BFBSA) which would require signatories to fit out their suppliers' premises to full safety standards.
On Tuesday, Carrefour, the world's second largest retailer, Benetton, Marks & Spencer and El Corte Inglés, the Spanish department store chain, joined major retailers like H&M and Inditex, the parent of Zara, in signing on to the safety agreement.
