If Mr Cossey is not located, the search area will be extended to include the Bromley and New Brighton areas in Christchurch.
Businesses in Christchurch's eastern suburbs were asked to check any outbuildings for any signs of Mr Cossey before they locked up for the summer break.
Anyone who had seen or heard from Mr Cossey were asked to contact police immediately.
Mr Cossey was described as European, 187cm tall, of a medium build with short brown hair.
At the time of his disappearance he was believed to be in good health with no known medical conditions and his family said it was out of character for him to not be in regular contact with them.
He was last seen in Eastgate Mall at approximately 1pm on December 5 wearing a black hoodie with a square orange design on the back, a white t-shirt, black jeans, dark shoes and with sunglasses on his head.
He was not believed to have access to a car and it was not known whether he had changed his clothes since his last confirmed mall sighting.
Mr Cossey moved to Christchurch from Auckland a few weeks ago to take up work related to the rebuild. However, he has not been in contact with his employer, Mercer Stainless, or returned to work since he left approximately 30 minutes after he arrived at 7.15am on Friday December 5.
He did not know the area well and police and his family had serious concerns for his wellbeing and asked anyone who has seen or heard from him to contact police urgently by calling 03 363 7670.
Alternatively, information could be provided anonymously through Crimestoppers on 0800 555 111.