The mother was horrified as Matthew Jenart, 28, said he was 15 and made the sick suggestion.
She posed as her daughter when the girl received a Facebook message from someone she did not know.
The mother called police after the conversation became sexual.
Unemployed Jenart, of Thornaby-on-Tees, was arrested in December then brought to Teesside Crown Court where he admitted attempting to incite a child under the age of 13 to engage in sexual activity.
Jenart, who said he would not have taken matters further, was handed a three-year community order, put on the sex offenders' register for five years, banned from working with kids, and ordered to have treatment.
Judge Mr Recorder Adams said the Facebook chat was 'disgusting' but did not jail Jenart because it was 'not clear' what the pervert's intentions were.
The girl's mother, 28, said: "His intentions seemed clear to me – he should be behind bars where he wouldn't be a danger to any more young girls.
"It's terrifying to think what might have happened."
THE FACEBOOK CHAT
Mum (posing as daughter): Who are you?
Jenart: Matt who you xd
M: you tried adding me??
J: I know to friends if you want to be
M: but i dont even know you?
J: I know lol but we can get to know each other
M: How old are you? why do you want to be friends with me i'm only a kid
M: you dont look 15
J: Ok kool what you upto xx
M: just chilling, listening to some music u?
J: Kool watching the hulk xx
M: boring lol
J: Ok lol thanks so you got bf
M: No am too young
J: Ok kool who you with
M: am in my bedroom on me own
J: Kool you want fun
J: Naughty fun lol
M: what do you mean?
J: I mean naked fun
M: im only 11
J: Lol it only fun try it you will like it xx Whst you upto tomz
M: nothing much
J: Kool so you going to have fun xx
M: no am too young and your too old
More on Parentdish: Advice on keeping your children safe online
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