The American predators have laid waste to fish and vole populations in recent years and infiltrated every waterway in Edinburgh.
The carnivores, which were imported in 1929 to set up fur farms and are notorious for attacking native wildlife, have flourished in the waterways of the Water of Leith, Leith Docks and the Union Canal.
A report to the council estimates it would cost £4,200 per kilometre to eradicate the mink, and that there are 72kms of watercourse habitat for the species. It would take up to five years to trap and humanely kill the mink – described as “indiscriminate” killers – and cost more than £300,000 per year.
Mark McInnes, Conservative councillor for the Meadows and Morningside, said a number of local residents have raised concerns about the creatures, which can be vicious when confronted.
“I propose that there are further reports on how to deal with this ongoing problem. I appreciate it is difficult to address because of the sheer numbers of them – there will be hundreds by now – and because of the way they are able to adapt. But people, especially along the [Union] canal, have said it has got much worse over the past few years.”
In his report to Edinburgh City Council’s environmental committee, director of services for communities Mark Turley wrote: “Mink are highly adaptable predators and can affect prey which do not form an essential part of their diet.
“Consequently, a decline in the population of one prey species will cause mink to switch to an alternative prey.”
He added: “An eradication programme would need to be long-term for the same reason.”
Last month, one Edinburgh resident, retired manufacturing manager Alistair Lucas, reported having hundreds of pounds worth of fish go missing from his garden pond in East Craigs.
His collection of four large koi carp, each more than 20 years old, disappeared earlier this year despite being protected by netting.
“It had to be something that could swim in the pond, which cats don’t do,” Lucas said at the time.
Councillors will decide whether to approve the cull on Tuesday.