The SNP opposition in Glasgow has agreed to table a motion on the subject next month, forcing the full 79-member council to debate and then vote on Atos's involvement.
The French IT giant, which also sponsored the London 2012 Olympics and Paralympics, has been heavily criticised over the benefit tests carried out by its subsidiary Atos Healthcare for the UK Department for Work and Pensions.
Atos Healthcare is paid £112 million for conducting work capability assessments on the sick and disabled, including cancer patients, and also has a £400m deal to assess mobility benefits. Those failing the tests face losing benefits.
Last week, shadow work and pensions secretary Liam Byrne told the Labour conference that Atos should be sacked, calling it "part of the problem, not the solution" to welfare reform.
Critics say the tests performed are flawed, degrading and inefficient, with one in six passed as fit to work winning an appeal.
The SNP motion before the Labour-run council regrets that Atos is helping to implement the Coalition's "iniquitous welfare policies" and demands that the council's top official writes to the chief executive of Glasgow 2014 "seeking the removal of Atos as a corporate sponsor of the 2014 Commonwealth Games".
Atos is due to supply software to accredit up to 70,000 athletes, volunteers and officials for Glasgow 2014, and run the Games website.
As the council is on the Glasgow 2014 organising committee and is footing 20% of the £468m public bill for the Games, a vote to dump Atos would be impossible to ignore.
However, if Atos was dropped, it could create major financial and technical problems.
Acting SNP leader Billy McAllister, who is tabling the motion, said he wanted to build a cross-party consensus on removing Atos before the debate and vote on October 31. Labour councillor Marie Garrity has already denounced Atos as unfit to be a Games sponsor.
McAllister said: "Atos is a highly contentious issue for councillors, because we all have constituents who've suffered at their hands."
Deputy First Minister Nicola Sturgeon last year welcomed Atos's sponsorship as "a significant step forward for the Games". Her constituency surgery in Glasgow Southside was later picketed by anti-Atos demonstrators.
A council vote is also potentially embarrassing for Scottish Labour leader Johann Lamont, whose husband, Councillor Archie Graham, is the city's executive member for Glasgow 2014 and, like Sturgeon, has publicly praised Atos.
A spokesman for Atos said: "Our dedicated staff are working tirelessly to provide Games management systems and Games information systems to help deliver a first-class Games that will showcase the best of Scotland to the world."
A Glasgow 2014 spokesman said: "We are very proud to have global IT experts Atos as part of Glasgow 2014's Sponsor Family."
A council spokesman said: "Members will consider this is in due course."