The contract, which runs form February until October next, has been tendered by the Department of Arts, Heritage and the Gaeltacht.
Among those animals on the list to be trapped include feral mink, grey crows and foxes.
The National Parks and Wildlife Service will provide Transport for the person who wins the contract.
The contract has been put up because of a general rise in the number of such predators in recent years leading to the need for an annual cull of such creatures.
The rise in the number of wild mink is believed to be related to a massive escape of mink form a farm outside Ardara in 2010.
IT is understood that at least 5,000 of the farmed mink escaped in what some believe was a malicious attempt to free the creatures.
Those interested in trapping the predators for the specified season must have their own licensed shotgun or rifle.