Dolly could snatch the Guinness Book Of Records title from Lucky, a 23-year-old ewe that died in 2009.
Owner Sharon Moore adopted Dolly aged 16 when her owner became too ill to care for her.
Dolly the sheep has lived to the grand old age thanks to a diet of apples at the Moore Racehorse Trust animal sanctuary, in Ditchling.
Sharon, 46, said: “We got Dolly from a lady who was terminally ill.
“She had leukaemia and passed away before she could see Dolly in her new home.
“She was 16 when we got her and that was seven years ago. Everyone that sees her can tell she’s really elderly.
“She looks really frail and she’s a bit unsteady on her feet but she’s still very strong.
“She’s amazing. Year after year I think, ‘This will be her last summer’ but she just keeps going.
“She’s just got such a strong will to live.
“She has a normal diet of sheep food, hay and grass, but she really loves apples - perhaps that’s her secret to a long life.”
Sharon, a retired owner of a gardening business, runs the sanctuary with husband-of-18-years Gary, 56.
They have four grown-up children between them but love extending their family by rescuing animals.
Dolly, believed to be a cross breed, came to them in 2008 along with three other sheep and a goat and now needs special treatment in the winter because of her seniority.
The previous record holder, the unfortunately named Lucky, died in a heatwave in 2009 at her farm in Lake Bolac, 57 miles west of Melbourne, in Australia.