Members of the British Medical Association (BMA) have said the NHS should stop funding such hospitals, arguing there is no evidence of their effectiveness.
The chief executive of the health board, NHS Greater Glasgow and Clyde, Robert Calderwood, said that last year one health board had decided to stop referring patients to the hospital.
And he warned that, if others follow suit, he will have to look at how much the hospital is costing the health board.
With cuts of about £50m to find in the next financial year, the BMA is calling for funding to be withdrawn.
Mr Calderwood said: “You could be forgiven for thinking it is a no-brainer.”
On the Gartnavel General Hospital site, the homeopathic centre is one of four funded by the NHS in the UK.
It treats seriously ill patients from across Scotland using conventional medicine and alternative therapies such as acupuncture.
Staff aim to look after the whole person rather than their individual ailment.
Mr Calderwood said NHS Highland had agreed not to commission the service for their patients.
He added: “We know other health boards are considering the whole clinical effectiveness debate.
“They have not said publicly yet where that debate will take them.”
He acknowledged that, when the board consulted on closing overnight beds at the hospital in 2004, there was a high-profile campaign by patients to keep the service and it was ultimately saved.
Matt McLaughlin, Glasgow health organiser for the public sector union, Unison, said: “When I speak to people who work there or benefit from the hospital, they tell me that it works.
“If it works, that is the no-brainer for me.”
The hospital was opened in a Victorian mansion in Great Western Road in 1914 and moved from there to a former industrial site at Gartnavel in 1999.
It receives about £1m each year in government funding, and carries out an average of 10,000 consultations each year, also taking referrals from The Beatson Institute for Cancer Research.
In recent years, the hospital has also been known as the Centre for Integrated Care to reflect the holistic approach it offers.
Treatments are tailor-made for patients, and are usually a combination of counselling, physiotherapy, diet and alternative therapies such as acupuncture, meditation and homeopathy.
It is not the first time the homeopathic hospital has faced a funding threat.
In May 2004 the Greater Glasgow Health Board announced it was considering cutting the hospital’s 15 overnight beds.
A massive campaign was launched to save the hospital and a petition with 22,000 names was handed over before the board bowed to public pressure.
Last year top alternative health expert Dr Jan de Vries said closing the hospital would amount to taking away the public’s freedom of choice.
Meanwhile, Mr Calderwood has also warned that new targets to cut waiting times for NHS treatment risk stifling improvements to medical care in Scotland.
He said surgery was now available so soon on the health service it was almost as swift as the care on offer at the private hospital, Ross Hall.
Patients, he said, were already asking for procedures to be delayed because the dates offered clashed with plans they had made in the near future.
He argued against setting further reductions in waiting times for diagnostic tests and procedures after the end of this year, saying doctors felt other improvements to care were more important.
He said: “We are already getting patients saying: ‘I didn’t think it was going to be that quick.’
“To make it quicker would require a real debate with clinicians about the opportunity costs, because there are new services they want to deliver.”
Mr Calderwood said that, while his budget will increase by 1% next year, bills for essentials such as prescription drugs will increase significantly more.
This means he will have to find cuts of £45m to £51m, just to keep services as they are at present.
The Scottish Government has set a target of cutting the total waiting time from GP referral to hospital treatment to 18 weeks, which is due to be met by the end of this year.
This means NHS GGC will have to save even more money in other areas to fund the extra work required to hit this goal.
Mr Calderwood said: “We would expect to have to add another sum of money to the £45m to £51m I have talked about to recognise that productivity increase.”
He also revealed that a review of all services across the Greater Glasgow and Clyde region of the NHS will be launched next year.
It will be the first time the board has looked at the spread and capacity of its hospitals since the Clyde area was added to the city’s health board.
The last acute services review covering Greater Glasgow in 2002 closed the A&Es at Stobhill Hospital and the Victory Infirmary, causing ongoing controversy.
The new review will consider how to take services forward after 2015, when the new £100m children’s hospital will be completed on the Southern General campus, and the Southern General will house one of the largest adults’ hospitals in the UK.