Jade Anderson was found alone with five of the animals at a house she was visiting in Chaucer Grove, Atherton, Wigan, on Tuesday.
Four dogs, believed to be two bull mastiffs and two Staffordshire bull terriers, were shot by police marksmen. A fifth dog was contained.
"They were confronted by a number of dogs that were aggressive and out of control," a Greater Manchester Police spokesman said.
The dogs - which are not banned under the Dangerous Dogs Act 1991 - belonged to the owner of the house, Beverley Concannon, the Telegraph reported.
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The owner is unlikely to be prosecuted prompting calls by MPs and campaigners for a change in the law, the paper said.
Jade was a friend of Concannon's daughter, Kimberley, 16, who is believed to have been in a neighbouring house - heating a pie - when the attack took place.
Chloe Dewett, 12, a friend of Jade's who lives near the house where the attack took place, said: "If you walked down the alley next to the house, you walked on the far side, away from the fence, because they were always jumping up and barking.
Anne McIntosh, a Conservative MP, said that dog attacks on private property should "carry the full force of the law and all the criminal sanctions that would take effect if the attack happened in a public place."
The Department for Environment, Food and Rural Affairs estimates about 210,000 people are attacked by dogs in England every year.
Five children and one adult have been killed by dogs on private property since 2007.
Jade's school, Fred Longworth High School, said staff and pupils were "all deeply shocked and saddened".