Council leaders could seek to take a bill through Parliament so the city council is no longer obliged to provide a livestock market within Norwich's boundary.
An Act of Parliament dating back to 1984 means Norwich City Council has to provide a site for such a market and it currently meets on land at Hall Road.
That land is part of 19 acres which entrepreneur Graham Dacre bought in 2010, but which he leases back to the council for use by the livestock market.
But the city council says it can save £32,000 if it did not have to provide a site for the livestock market and in its budget for the next year, are proposing setting aside £42,000 to use to remove the act which obligates it to provide it.
Alan Waters, deputy leader of Norwich City Council, said: 'For some time we have been looking at ways to extinguish the Act of Parliament which means we have to provide a livestock market.
'The world has moved on since that act and it doesn't make sense for that market to still have to be provided within the city's boundaries. What we are keen to do is have some sort of food hub off the southern bypass. I think that would be much more relevant.'
Last year, it emerged Norwich Livestock Market could move to Easton under plans for thousands of homes and new employment opportunities to the south and west of the city.
A 40 hectare site to the west of Easton has been earmarked in South Norfolk site allocations plan for a Norfolk food and farming hub to also include the potential relocation of the livestock market.
Mr Waters said: 'What are are exploring is spending some money to get legal advice on how we can remove our obligation. If we are able to release that obligation there will be some finanical benefits.
'We may spend up to £10,000 to explore it and we may well have to put it through Parliament, seeking a private bill to extinguish it.
'The £42,000 is what it could cost us to go through that whole process.'
But David Ball, operations manager for the livestock market, said he had heard nothing about the council's plan.
He said: ''Our understanding is that they have a 99 year lease on the existing site, so I don't really see how they can walk away from that.
'From the point of view of auctioneers and farmers, we would be very disappointed they are trying to get out of theis obligation.
'On a Saturday we have about 250 people at the market. It's a social meeting point for the agricultural industry and that's really important.'
The city council's budget, which includes £2.5m worth of savings, is due to be discussed at a meeting of the controlling Labour cabinet tonight. A final decision on it will rest with the full city council, which meets next Tuesday.
The budget also includes proposals to increase the city council's share of the council tax by 1.95pc. That would mean, from April, somebody living in a Band D property in the city would have to pay £230.27 into City Hall's coffers, an increase of £4.40 on the current level.
That comes on top of the £3.84 extra which people will have to pay to Norfolk police, after the new police and crime commissioner decided to increase the share which goes to the force by 1.965pc.
Norfolk County Council has announced there will be no increase in its share of the tax, which is due to be ratified when the county council agrees its budget on Monday.
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