"We're in bits, the whole country has helped us and is supporting us. I haven't slept in four days. Natalie (Tia's mother) is in bits. The police have done everything."
The Sun newspaper has offered a £25,000 reward for information that will lead to police finding the 12-year-old.
It was believed the last person to see Tia was Mrs Sharp's partner, Stuart Hazell. But Mr Niles said he was unsure about that, adding: "The last time I saw her was on Thursday morning before going to work (at the family home in Mitcham). She had a friend stay over. She was good as gold.
"I know I am not her real dad, but I have been there since day dot. I have fed her and bathed her. I just want her home. When she left the house she shouted 'Bye' and 'See you by six'. She always takes her phone but it was dead."
Mrs Sharp, speaking from her terraced home, said she hoped an image of her granddaughter taken outside the nearby Co-op on Thursday would jog people's memories and bring forward new information.