The last place in England to offer publicly-funded homeopathy could stop providing the practice on the NHS.
Bristol's clinical commissioning group (CCG) is meeting to discuss ending NHS-funded homeopathic treatment except in exceptional circumstances.
Homeopathy is based on the idea "like cures like", but many scientists say patients are only getting sugar.
The British Homeopathic Association said its treatments were of "enormous value" to patients.
Since homeopathic treatments stopped being provided at the Royal London Hospital of Integrated Medicine in April, referrals for NHS treatment by homeopathic practitioners have only remained possible in Bristol and at the Glasgow Centre of Integrative Care.
'No good-quality evidence'
In Bristol, the NHS homeopathic service is delivered on behalf of the University Hospitals Bristol NHS Trust by the Portland Centre for Integrative Medicine in Clifton.
The trust says homeopathic medicine has been available in Bristol since 1852.
A 2010 House of Commons report found homeopathic remedies performed no better than placebos – dummy treatments.
In 2017, NHS England recommended that GPs and other prescribers should stop providing it.
It said: "There is no good-quality evidence that homeopathy is effective as a treatment for any health condition" while the National Institute for Health and Care Excellence (NICE) does not recommend using homeopathy for any clinical condition.
But the practice remains popular with some patients seeking alternative or complementary treatments.
The governing body of Bristol, North Somerset and South Gloucestershire (BNSSG) CCG, which oversees NHS services in the area, said about 40 patients per year received NHS-funded homeopathic consultations and the cost in 2017-18 was £109,476.
It needs to make savings of £37m in the coming financial year.
"This equates to around a further 22 hip replacements or 170 cataract operations," it said.
The CCG will consider the report recommending restricting referrals, at its public meeting on Tuesday.
If approved, clinicians would in future need to set out why their patient was "clinically exceptional" and required the treatments.
'Enormous value'
"Staff and clinicians from across the CCG have closely examined the full range of clinical evidence available from both sides of the debate, consulted with local people, clinicians, patient groups and providers of homeopathic treatments," said Dr Peter Brindle, BNSSG medical director for clinical effectiveness.
But Margaret Wyllie, Chair of the British Homeopathic Association, said: "This demonstrates a lack of long-term decision-making by NHS bosses and helps to explain the ongoing NHS crisis.
"The amount of money spent on homeopathy by Bristol CCG is a tiny fraction of the local NHS budget but is of enormous value to the patients who benefit from the treatment, many of whom are elderly, and have chronic health conditions.
"The CCG should evaluate the impact on the future health, and costs to the NHS, for the homeopathy patients once the service is removed."
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