Allan Whittern ran the grocer's store in Suffolk Parade from 1932 until his death 50 years later, in 1982.
Following its closure in 1991, the door painted with his father's likeness was donated by his son to the Wilson Art Gallery and Museum in the town.
The Cheltenham Trust, which runs the gallery, wants to restore it for an exhibition later in the year.
His daughter-in-law, Thelma Whittern, said it was painted with Mr Whittern's portrait after he refused a request by a Whitbread representative to place an advert on the warehouse door.
"The chap said 'well what can we put on?' and Allan promptly replied 'you can put me on'. And so the chap did," she said.
She said since it disappeared, people have asked after its whereabouts.
"People used to pass by in semi-darkness and see the portrait there and [say] 'goodnight Mr Whittern', thinking he was coming out of the warehouse.
"Since he's gone we've been asked by so many, 'where is it? What have you done with it? You haven't destroyed it?"
A crowdfunding campaign for donations has reached more than half of the Â£3,000 needed for the work to be carried out.
A further Â£1,400 needs to be raised by Friday.
The trust's Chloe Moorhead said: "Championing Cheltenham's rich heritage is of huge importance to the trust and to the town.
"This is a fantastic opportunity for people to play their part in preserving an important part of Cheltenham's art history for generations to come."
A portrait of a well-known Cheltenham grocer which was painted onto his shop door in the 1960s could be restored.