They also thanked Farnham's fans for their enduring support.
"The Farnham family want to acknowledge and thank everyone for their ongoing messages and well wishes that have been shared throughout the last week," they said.
"It really lifts our spirits knowing that everyone is thinking of John."
On Monday, entertainment reporter Peter Ford said Farnham would need some time to recover.
"This is going to be a very long process for John. He was always expected to be in ICU for weeks. Six days later and he's still there," he told Sydney 2GB host Ben Fordham.
Previously, Fordham hinted that the 'You're the Voice' singer was facing a lengthy recovery process.
"Doctors may have to insert a tube into his windpipe as part of his recovery," he said on Wednesday.
"He'll need a feeding tube and he'll need rehab to help him chew and swallow again, he'll spend weeks in hospital recovering."
Although the musician doesn't have social media himself, a collaboration between Ford, Angela Bishop and Richard Wilkins allows people to send him messages of support.
Dubbed weloveyoujohn.com.au, the site was done with consent from his family and will be shared with Farnham and his family "when the time is right".
"It's a more professional way of going about things. It's a place for people to send John a message," said Ford.
Sharing insight into the singer's health struggles, his longtime friend, Derryn Hinch said his friend had "smoked too much" for years. According to Johns Hopkins University, the act can increase a person's chance of developing oral cancer 10-fold.
However, Hinch told The Big Smoke a simple plea made him quit smoking cigarettes.
"For years, John smoked too much. He only stopped when a precious son said, 'Daddy, I don't want you to die.' So, he switched to cigars," Hinch wrote.
