Green was wearing grey track pants with large holes down the front of the legs and a grey zip-up hooded top. He was no longer carrying his backpack.
Land Search and Rescue teams have searched the area but have not found Green.
Police said they continue to conduct area inquiries, including speaking to residents in the area and appealing for CCTV footage.
“We ask for anyone who may have CCTV or other cameras in the area to please check to see if there is any sign of Nathan from Tuesday, 14 April to date,” they said.
“If you have seen Nathan, or have any information that may help us find him, please call 111 immediately and reference file number 260414/6742.”