Sree Sanatan Mandir in Leicester made the announcement a day after Bank of England confirmed that there is a trace of tallow in the "polymer pellets used in the base substrate of the polymer 5 pound notes".
Vibhooti Acharya, president of the temple, said it has caused "anger" among Hindus, many of whom tend to be vegetarians and do not believe in harming animals.
She said the temple's committee was considering a ban on the notes.
"No-one was informed and it's been thrown upon us. We don't have the opportunity to choose. There needs to be a decision made between committee as to whether we accept five pound notes in religious ceremonies in future. We have to give a reasonable amount of time for resolve, [but] we can't really take any drastic steps because it's just not practical," she told BBC.
Donations are taken at the Shree Sanatan Mandir temple for charitable causes in the community.
The city of Leicester has one of the largest populations of Hindus in England and is famous for hosting the biggest Diwali celebrations outside India.
The fatty substance used in the notes is traditionally derived from beef or mutton and sometimes pork.
The new notes with an image of Britain's war-time Prime Minister Winston Churchill became legal tender in September this year.
The production process was revealed on Twitter this week by Bank of England in response to a question.
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