James McEwan, aged 67, had not been seen since 9am on Saturday 29 October 2011 when he was at his home on Cottesmore Drive.
James, sometimes known as Jimmy, has been ill recently and received hospital treatment earlier in October for a chest infection.
After being discharged on Wednesday 26 October, he was seen at home by Manchester City Council staff three times a day to help him settle back in at home.
James was still feeling ill when he was last visited.
James has a Staffordshire bull terrier called Bruce that he normally walks each morning around the Harpurhey Road area and then takes him up to the shops on Cheetham Hill Road.
Bruce has had to be put into kennels while James was in hospital and remains there.
James has left home without his key.
Officers have been out handing out leaflets with pictures of James on and putting up posters as well as appealing through the media.
Following an appeal to the public last week, a shop worker came forward to say she had seen him with a woman on Crescent Road near to Cheetham Hill Road / Bury Old Road at 6.45am on Monday 31 October or Tuesday 1 November 2011.
He was walking along the pavement at the side of Poundstretcher with a white woman, aged in her mid 60s, of normal build with grey bobbed hair. She had a skirt to her calves, a coat that came to her mid thigh and he was carrying a bag.
Officers are also keen to trace her.
James is a white man, aged 67, 5ft 9in tall, of slim build and is usually unshaven. He tends to wear a grey fleece, grey tracksuit bottoms and trainers.
Detective Sergeant Jim Slack, based at North Manchester CID, said: "James has been poorly and is devoted to Bruce and we know that coping with his illness and being apart from his dog has been a huge struggle for him.
"James' family and friends are extremely worried that he is missing when he is so vulnerable.
"This new sighting has given us the hope that he might be staying with someone and being looked after: so we're keen not only to hear from James but also this woman, just to know that he is safe and well.
"If you have seen him, please contact us."
Anyone with information is asked to call officers in North Manchester on 101.