Scottish Care, which represents private care home owners, said the local authority was insisting on "derisory" rates that would risk homes going bust or force them to cut corners and reduce the quality of care.
A council procurement exercise carried out by the council ended at noon yesterday. All local authorities will break away from a national deal on care home funding by the time health and social care is integrated in April 2015, but Glasgow is the first to do so.
Scottish Care said the offer, which involves the council buying about 3600 care places from 85 care homes at a set rate, was too low and would set an alarming precedent for other councils.
The industry body is seeking a judicial review on behalf of its members. It says the tendering process, under which care providers were invited to join a list of registered providers of care, was flawed. Meanwhile, Scottish Care members have instructed lawyers to examine whether a process the council plans to use to rank care providers and allocate work to them is fair.
Care home owners are also angry that the council spends much more on its own in-house care provision than it is willing to pay for external care.
Scottish Care said that while the tender offers homes £510-£590 per person per week for care, the council spends more than £800 per week on those in its own homes. Meanwhile, the council is offering a 1 per cent increase in funding per year over four years, while homes expect their costs to rise by 12 per cent in the same period.
Chief executive Ranald Mair said the offer was derisory, adding: "Glasgow care home providers have been more than willing to engage in talks with the council to reach a fair agreement, yet officials have remained committed to dictating to rather than consulting care homes on this matter."
He said the tender was moving care provision backwards, adding: "The care home sector in Glasgow, and across the country, is at a crucial juncture.
"There is a need for real investment in quality, service improvement, and future development. We can't go on saying we want people to look after frail and elderly adults on the minimum wage."
Mr Mair said some care providers had refused to bid to join the Glasgow framework, while some other larger ones had tendered, but priced their services at a higher cost than the council has indicated it is willing to pay. However, he said procurement rules had prevented a coordinated approach.
He added: "Despite our efforts at negotiation, the only way the council is prepared to even consider addressing the significant issues within this tender is if the tender fails and the council has to start again or if the results of our legal actions forces them to do so. There appears no willingness to change tack at this stage."
After setting up a task force to look at the funding of older people earlier this year, the Scottish Government published a report that said inadequate funding for older people's care could force firms into administration, lead to staffing problems, cut the quality of care and cause bed blocking.
A council spokesman said: "We have not received any court documents in relation to this matter, therefore, it would be inappropriate to comment at this stage."