Unite has agreed to mediation after talks with the city council broke up after 45 minutes on Wednesday.
The long-running dispute, now in its sixth week, has seen uncollected waste pile up in some areas.
The leader of Birmingham City Council says refuse collectors need not lose a penny.
Unite says Birmingham City Council's leader told the BBC nobody needs to be losing income.
Bin workers remain in a stand-off with the council after an all-out strike started on 11 March.
Bin workers remain in a stand-off with the council after an all-out strike started on 11 March.
The rejection brought pressure on ministers to get tough on their 'paymasters', with accusations that Labour's inaction was taking Britain 'back to the 1970s'.
The health secretary says he is concerned about the "poor conditions" on the streets of Birmingham.
The health secretary says he is concerned about the "poor conditions" on the streets of Birmingham.
Bin bags have continued to pile up in many areas and attract rats and other vermin as the strikes continue