"The woman in the photo may be able to assist us trace Mr Wiremu's movements and enlighten us as to his wellbeing at the time of their interaction," she said.
"There is no suggestion she had anything to do with his subsequent decline in health. We simply want to identify and speak with her to see whether she can help us."
Officers have been tracing Mr Wiremu's movements in the city between 9am and 1pm on Tuesday, May 12 and have appealed for anyone who may have seen him in the vicinity of the Auckland Transport carpark on Victoria St or on Lorne St, High St, Kitchener St or Queen St, to contact them.
Mr Wiremu was described as being of a solid build, with a shaved head and long white beard. He was wearing grey tracksuit pants with two white stripes down the legs, a black polo shirt, a grey long-sleeved jersey with a black panel down each side, and grey/black slippers.
He was also carrying a manila or plastic folder containing documents in a bag, which police have yet to locate.
Anyone with information about the woman, or Mr Wiremu's movements, is asked to contact Detective Sergeant Marcia Murray on 021 191 2693, email on marcia.murray@police.govt.nz, or anonymously contact Crimestoppers on 0800 555 111 quoting Operation Oregano.