The Warrnambool Art Gallery was dedicated as a memorial to the clothing entrepreneur, and the ageing building is in need of a major upgrade, but a possible relocation to Cannon Hill has been controversial.

Against officers' recommendations, councillors voted 4-3 to complete a business case for Cannon Hill rather than for the current site which has prompt opponents to start a petition.

The business case - which will cost more than $100,000 - is being funded by the Victorian government, the council and a $20,000 commitment from the FJ Family Foundations.

Despite the funding commitment, Fletcher's grandson David Jones said the foundations had no input into which site was chosen for the business case but they were happy to explore Cannon Hill as an option.

"Our funding hasn't been tied or biased," he said.

Mr Jones said Cannon Hill was a "remarkable spot" and called on the community to look at the alternative site before saying 'no'.

"We're really thrilled that the council has landed where they have to at least consider it," he said.

"With the appropriate, intelligent and sensitive architecture, I'd like to think it could really activate that site and do a building that's embedded into the landscape.

"Let's just let the process run its course.

"If the business case comes back saying that this site doesn't work or the Indigenous community think it's a disaster and the broader community think it's a disaster then obviously it won't proceed."

Mr Jones said it was very important Indigenous leaders in the community were supportive of a business case for Cannon Hill.

"And we understand that they absolutely are," he said.

"Warrnambool has got a wonderful Indigenous heritage. Grandpa used to spend time at Framlingham. He had a great respect for the Indigenous community.

"What is exciting is this site could really help re-engage that community with the site too."

Mr Jones said he acknowledged he no longer lived in Warrnambool and wanted to make sure his comments didn't come across as the third generation of the Jones family "telling Warrnambool what Warrnambool should do".

He said he just wanted to say "hey, just let the process run its course and let's let our imagination run for a bit before we just say 'no'."

Mr Jones praised the leadership of council and called on people to give the business case a chance.

"We need a new gallery and so why wouldn't we use forward thinking outside the box and potentially putting it at a really interesting site?" he said.

"I think we can all agree that the current gallery is not fit for purpose and that we need a new gallery. Let's explore what the best alternatives might be."

Mr Jones said the family's three philanthropic entities - which all came under the FJ Family Foundations umbrella - focused their activity on projects in the Warrnambool region and they would be keen to help fund a new art gallery.

"We said that because the building is a memorial to Grandpa we would be delighted to back that development activity," Mr Jones said.

For the past year the foundation has funded a one-day a week role at the gallery which is also tasked with helping to raise philanthropic money for a new gallery "wherever it may be".

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