A shortage of staff and lack of resources is forcing them to turn people away.
The Scottish Housing Regulator has already raised "significant con-cerns" about the council failing to meet its legal duty to homeless people.
And it demanded Glas-gow take immediate action and make improvements as quickly as possible.
One worker from one of the city council's homeless-ness teams contacted the Evening Times.
She claimed staff are coping with a large work-load and are forced to tell people each day that no accommodation is available for them.
The woman, who asked not to be named, has worked for the city council for a decade.
She says the department is suffering from staff shortages and lack of resources to help people in need.
The woman said: "Each day we are turning away people - mainly single men.
"We always manage to accommodate people with children in temporary furnished accommodation or bed and breakfast.
"But single males, single females and couples get turned away on a daily basis. The number varies but there can be easily six people a day and the same six will turn up day after day looking for help.
"We cannot provide them with accommodation but give them bus tokens so they can try and find somewhere themselves which is absolutely ridiculous.
"It is hard to turn people away. What can you say to a grown man in tears in front of you because he has nowhere to stay?
"They will sit in the waiting room and refuse to go in the hope you will phone the police so they will be lifted and have somewhere to stay.
"The service is at break-ing point. I've never known morale as low as it is."
The woman said staff are having to deal with lack of permanent accommodation for the homeless and staff shortages.
She added: "There is a log-jam in accommodation and it is increasingly difficult to move people into permanent accommodation because of the lack of one- bedroom properties.
THAT is down to the impact of the bedroom tax and the demolition of a lot of the housing stock in the city."
Staff have to investigate the circumstances of each new person reporting as homeless, but say the scale of the workload means they are struggling to find time to do the necessary checks in the set time of 28 days.
The woman said: "The council has to give us the resources to do our job properly."
In September last year, more than 100 members of the city's homeless team walked out in a dispute partly provoked by increased workloads.
Unison convener for social work Ian Leech said: "The walkout was sparked by a grievance which went in from the East community casework team about the lack of staffing.
"Staff diary in activities for the days they are on casework which gives them time to manage cases but the system has fallen into disrepair because of lack of staffing.
"Because of the increas-ing number of homeless-ness cases coming forward, the economic crisis and the bedroom tax, pressure has come to bear on the service.
"If people don't present with immediate problems they are told to come back when the problems are immediate and are being turned away."
A city council spokesman said: "We fully acknowledge there is significant pressure on our homelessness service with the overall shortage of suitable accommodation a particular challenge.
"The council depends on registered social landlords to provide accommodation for people affected by home-lessness but insufficient numbers of homes are being made available.
WE ARE working on an action plan which includes significant capital investment in two new homelessness units.
"Talks with housing providers are also on-going which we hope will secure access to a substantial num-ber of additional flats for the homelessness service. We continue to work with voluntary organisations to address homelessness issues in a range of ways.
"Our street team service has been enhanced to ensure rough sleepers are being directed to appropriate support but people affected by homelessness can have complex needs and be difficult to engage with.
"A far greater emphasis is now also being placed on preventing homelessness and this approach is helping to reduce significantly the overall number of homelessness applications.
"We believe there are sufficient resources within the homelessness teams to deal with demand. The workload for staff is in line with that experienced in other local authorities."