The trade union Unite says the cabbies it represents are taking a 'huge hit' from increasing costs.
They’ve demanded an extra 50p be added to the taximeter at the start of each journey.
The city council, which regulates hackney carriages, has agreed to consult over the possible increase.
A letter to leading council figures from Unite’s Leeds cab section, said: “As you will be fully aware, we are in the midst of one of the hardest financial times that we can remember in living memory, with significant increases in the cost of not only fossil fuels, but electric charging PkwH (per kilowatt hour) and LPG (petrol) too.
"Drivers are taking a huge hit to their already beleaguered earnings due to not having the capacity to offset some of these costs.”
The letter, which was originally written on 21 April, but has only now been published by the council online, added: “It is always the case that no driver should be earning less than the ‘living wage’.
“Yet sadly, with these increases and the fortunate position like private hire to increase at will, drivers are now earning on average less than £8 per hour, not even considering other costs attributed that must be covered within that hourly rate.”
The union asked for the increase to be implemented with 'utmost urgency'.
The council, which licenses 800 hackney carriage drivers in Leeds, will engage with other parties, including passenger groups, before making a decision.
In a report responding to the Unite letter, the local authority said: “It is possible that fuel prices may fall in the longer term, but they have been increasing very rapidly in 2022, and may well continue to increase.
“A small fare increase of 50p per journey would go a small way to covering some of the increased costs.”
The proposed rise would push the price of the average two-mile journey up from £6.40 to £6.90. This would remain cheaper than the equivalent journey in a hackney carriage in York or Harrogate, the report said.
However, the council added that: “Higher hackney carriage fares are seen as unaffordable to people who regularly use hackney carriages.
“This may or may not result in objections to the proposed fare increases.”
Any increase would not affect private hire vehicles, which aren’t regulated by councils in the way hackney carriages are.
Hackney carriages differ from private taxis in that they can’t be booked by passengers in advance and their fares are fixed by local authorities.