Mr Hayward, aged 80, was last seen at 10.15am yesterday morning (Tuesday, 11 July) in the Southsea area.
He is described as white, 5ft 11ins, of slim build and has grey hair. He was last seen wearing navy blue shorts, a blue top, a navy blue waterproof jacket, white socks and blue shoes.
Together with his family police are growing concerned for his welfare.
If you think you may have seen him since he went missing or have any information about where he might be, please contact the police as soon as possible on 101 quoting 44230278225.
In an emergency dial 999.