Opposition politicians in the city want a study on the "suitability and relevance" of the eight twins, the reasoning behind the relationships and the motivation for retaining them.
Where the relationships have no current value to Glasgow the twinning agreement should be binned, they claim.
It follows years of concerns of expensive jaunts at public expense to Europe and Asia with little to show for it.
Benefits of links to Dalian in China, which has one of the world's most notoriously poor records on human rights, were cited by the council after it brought badminton coaches to Scotland.
The move by the council's SNP group also comes on the back of publication of a letter by Lord Provost Sadie Docherty to her counterpart in the Russian regional capita Rostov-on-Don, twinned with Glasgow since the tail end of the Cold War, criticising the country's clampdown on the promotion of same-sex relationships within schools.
Four of the remaining five twinning agreements, Turin, Marseilles, Lahore and Bethlehem, were struck during the current senior Labour councillor Liz Cameron's 2003-2007 tenure as lord provost. The first twin, Nuremberg, dates from 1985. Havana, which has never been criticised by Glasgow for its human-rights abuses, was twinned in 2002.
Ironically, the SNP's shake-up bid comes while Mrs Docherty will be visiting Rostov-on-Don.
Glasgow has been Scotland's most enthusiastic twinner in recent years. The arrangements have led to allegations of junketing by some city politicians. Edinburgh also has eight twins, some of which go back 60 years, though none has been formed since 1991.
The motion by SNP veteran John McLaughlin before next week's full council reads: "Council acknowledges that twinning agreements with other cities worldwide can be of immense value to Glasgow in terms of trade, education and cultural exchanges; however, council agrees to examine the criteria and motives for current agreements as to their suitability and relevance in today's world. Council therefore resolves to reform, where necessary, such agreements and where such agreements are no longer necessary or suitable to rescind them.
"Council also agrees that any future twinning agreements or memoranda of understanding shall conform to the reformed criteria and motivational reasons."
An SNP group spokesman said: "The recent concerns raised about Glasgow's twinning in different forums has brought to a head some long-standing concerns about current practice. It's time we review all arrangements to ensure they are for the best benefits of Glasgow and not just seen as some kind of badge of honour."
A city spokeswoman said: "This SNP motion will be put to full council next week when there will be an opportunity to fully debate the merits of twinning. It would be inappropriate to influence debate ahead of that."