The private member's Bill, from Bethnal Green and Bow MP Oona King, has government support after gaining backing from trade unions, business, councils and DSOs.
They agree 'quality, equality and workforce matters' should be considered, although detail on what this covers is yet to be agreed. Pay is expected to be the most difficult issue.
Ms King said the Bill would free councils from having to take the lowest bid, and was an important equality step.
The Bill will allow the environment secretary to introduce by regulation areas councils can consider in letting contracts. Part II of the Local Government Act 1988 currently disallows non-commercial considerations.
Local government minister Hilary Armstrong is consulting on suggested changes.