Northern Territory Senator Nigel Scullion says the key to capturing a band of rogue pigs on the loose in Darwin is to get them drunk.

The three pigs have been running rings around police and council workers for days, dashing across roads and exploring a local golf course.

One of the pigs, Wiggy, returned home this morning but police have told the ABC they have been given permission to shoot the other two fugitives.

Senator Scullion says he has caught a few pigs in his time, and says an alcoholic snack would be a simpler way to catch the pigs.

"Pigs, like anyone, it's Christmas time, they don't mind a drink, as long as they're off the road," he said.

"They should have used a bit of some mashed sweet corn, molasses and half a bottle of rum.

"They're big eaters and they obviously don't mind a tipple.

"And look that's the safest and the most humane way to deal with them, is to just give them a bit of a drink."

He says it would take a maximum of 45 minutes to catch the pigs using his method.

"You can just simply walk up, they are completely compliant, straight in the back of the paddy wagon and they can go and get processed," he said.

Authorities are arguing over who is responsible for catching the two remaining fugitives.

But the animals' owner, Vivienne White, who lives at the Minmarama Aboriginal Community, says she is willing to return them to the wild if they are re-captured.

"I'd love to get the other two back and take them back and let them go from where they came from," she said.

"I'd take them back out bush but I need the transport to get the pigs out there."

However, Ms White says she fears she may never get her lost pigs back after they went on a longer than usual wander.

"They normally go just across the road and back on Dick Ward Drive and come back," she said.

"But this time they kept on going to McDonald's - they must have smelt the food.

"I don't think they'll be able to catch them.

"They've gone wild now. So it's going [to] be hard."