The wolf has been roaming around the St. Margarethen area and has been spotted near houses, farms and children's playgrounds.
One-year-old Fritzi is said to have a shy and peaceful nature, but experts warn that he is still a wild animal and could pose a threat to humans, especially if he has not eaten properly for a few days.
Because of this, zoo keepers are stepping up efforts to get the wolf to return to his home as soon as possible.
Fritzi escaped from his enclosure in Styria when a violent thunderstorm washed away the plates on the floor which prevent the animals from burrowing into the ground. The crafty wolf then dug an escape tunnel and broke out from his enclosure.
His keepers had originally hoped that he would come back on his own, but soon realised he was enjoying his freedom too much. They have been setting traps baited with his favourite food to try and recapture him. But so far Fritzi has not been playing ball and experts think his recent discovery of a chicken farm may be why he is not responding to the bait.
Sonja Gollenz, who works at the Wilder Berg zoo where Fritzi is from, said that wolves do not need to eat every day. Instead they tend to gorge for a day until they are completely full, and can then go another couple of days before they need to eat again.
Keepers have also attempted to entice Fritzi by adding his sister Julia's scent to the food traps by putting her faeces inside them, in the hope was that this familiar scent would attract Fritzi to the traps. But so far he seems unimpressed by what they hoped would be an irresistible combination.
On Tuesday, Plan B was put into action - an attempt to anaesthetise Fritzi. Retired vet Joseph Cain lay in wait for him all night on the roof of a house near to the wolf's favourite snack bar - the chicken farm.
But Cain's rifle, loaded with a dart, only has a range of 20-30m, and he couldn't get close enough to the wolf to target him.
If attempts to capture Fritzi continue to fail and he becomes a threat to humans, then there will be no choice but to shoot him, experts have said. They will first have to seek permission from the mayor before doing this, and have stressed that this is a last resort.
By Claire Caruth.