Broagan McCuaig, 8, remained in Yorkhill Hospital last night, after having surgery for serious facial injuries.
She was reportedly attacked by two dogs, said to be American bulldogs, which were being walked by a neighbour, on Friday evening.
At the time she was playing with friends outside her home on Gartloch Road in Garthamlock, in the city's north east.
Yesterday, a police van was parked outside the flats while members of the community gathered nearby.
Neighbour James Moffat, 44, told the Evening Times local people were in a state of disbelief. He said: "It is a close community so it is hard to believe what has happened.
"We can't believe it could happen to such a lovely wee lassie. It could happen to anybody but it is horrible that two dogs can do such an amount of damage to a little girl.
"Other parents feel sick at what has happened, because it could have been one of theirs.
"It is just hard to believe that something like that could happen."
Shop worker James, who was at work when the incident happened, said they had heard from the family that Broagan was conscious in hospital.
Mum Tracy Cox, 36, and dad Neil McCuaig, 39, were at her bedside and James said they were too distressed to talk.
He said: "She's had a few operations since it happened and it is progress, but not much progress.
"Her face and her leg have the main injuries.
"She's conscious and there is a wee a bit of her old self coming through, but not much."
Another neighbour described Broagan as a "lovely girl" who was popular with other children.
Helen Edgar, 32, said: "Broagan was just playing in the back court and having fun.
"We are all hoping and praying now that she pulls through."
It is understood that the dogs belonged to the residents of a ground floor flat in the aera where Broagan and her family lived.
Earlier reports described how Broagan had been attacked by dogs which bit and shook her.
Their owner was unable to drag them away and Broagan was only saved when two passers-by stepped in to rescue her.
Police said they had charged a 34-year-old man and a 33-year-old woman with offences under the Dangerous Dogs Act.
A spokesman from Police Scotland said: "An eight-year-old girl has suffered serious facial injuries after being bitten by two dogs.
"Our inquiries are continuing."