Consultation on the future of wild boar in Kent and Sussex ends next week.
Possible control methods include tracking and trapping
The animals became extinct in the UK three centuries ago, but it is thought that 500 are living in the wild after breeding since escaping captivity.
Options include leaving the animals alone, eradicating them or managing the wild population while preventing new populations developing.
Wild boar in England have no natural predators except man and culls may be required to manage populations.
The main group of 200 feral wild boar is in the Kent and Sussex Weald, with about 300 more in Dorset, Gloucestershire and Herefordshire.
Wild boar can cause damage to crops, conservation sites, sports fields and gardens.
They can cause road accidents and even attack people. There is also a risk they could transmit disease to livestock, says the consultation document.
But it also says wild boar can have benefits on woodland.
It states: "The government recognises the problems posed by the newly-established wild boar populations as well as the potential benefits."
Public consultation runs until 6 January. Documents can be accessed on the Defra website.