Nick Makin said it was "not true" that his mother, Aileen Makin, had withdrawn the house in Bristol from the market.
"When you wake up to tabloids saying the house is now worth £5m you've got to think about what you're doing... but it's not changing anything," he said.
He added that he wanted the artwork to remain in place and be protected.
Mr Makin told BBC Radio Bristol the sale had been "put on hold for 48 hours" after the mural appeared on the side of the semi-detached house in Totterdown on Thursday.
The creation - entitled "Aachoo!!" - depicts a woman in a headscarf sneezing and her dentures flying into the air.
"It does increase the value, and you have to take a moment to think about it, but it's not changing anything in terms of the house sale for us," Mr Makin said.
He added that "nasty things" had been said about the family after it was reported by several newspapers and websites on Friday that they were pulling out of the sale of the £340,000 house.
"That's always going to happen with something like this. We've received a bit of abuse from it."
Mr Makin said they had put a piece of clear acrylic over the artwork and installed an alarm system to try to protect it.
"Not only has it not earned us £5m, it's actually cost us money," he said. "We think it should be protected and stay where it is."
He added that the family was "looking at getting a covenant put into the deeds of the house" to make sure the Banksy mural stays where it is.
"Or if it was to be removed, to be removed to Bristol City Council or the museum, so it can be kept in its condition and safe and in the right hands," Mr Makin added.
Asked what he thought of Western civilization, Mahatma Gandhi famously replied, “I think that would be a good idea.”