The 81-year-old comedienne is currently relying on a machine to keep her alive after she went into cardiac arrest and stopped breathing whilst undergoing minor throat surgery on Thursday, but her family are still hopeful that she will be able to pull through.
A source told TMZ.com: "The family will have to decide in the next couple of days whether to keep Joan on life support. The family remains hopeful that if they do decide to turn off the machines, she will make a turn for the better and fight through it."
The 'Fashion Police' host was placed in a medically-induced coma after she was rushed to Mount Sinai Hospital in New York when she suffered serious complications during an operation on her vocal cords at the Yorkville Endoscopy clinic on Thursday morning.
Joan's daughter Melissa, 46, thanked fans yesterday for their continuous support.
She said: "Her condition remains serious but she is receiving the best treatment and care possible.
"We ask that you continue to keep her in your thoughts as we pray for her recovery."
Joan's health scare came a shock to fans as she appeared to be in "good spirits" the night before the operation when she cracked jokes about death during a performance at Laurie Beechman Theatre on Wednesday night.
She told the audience: "I'm 81 - I could go at any moment. I could fall over right here and you all could say, 'I was there!' "
- BANG! Showbiz