Detectives said they had "concerns around the state of the body and the injuries" and revealed the teenager had been reported missing just 20 minutes before she was found.
A friend of the 16-year-old chillingly said Leonne "had gone to meet someone" before her body was discovered by a member of the public in an isolated pathway.
South Yorkshire Police have cordoned off two alleyways in Victoria Street, where 20 bouquets of flowers have been laid in tribute to the teen.
One card read: "To Leonne and family. Thinking about you, miss you so much. Sleep tight, fly high angel.
A man in his 20s, who wished to remain anonymous and said at the scene he was "deeply shocked" at the death of his friend.
He added: "I used to be neighbours with her and know her really well - she's a good mate of mine, is Leonne.
"We don't know what's happened, all we know is she went to meet someone - meet a bloke [man] - and now her body has been found.
"She met him off the internet - one of those dating sites."
Asked if he knew how Leonne had died, he added: "I don't know - all I know is the pathway is just a dead end and backs onto a few allotments down there."
Another local said that they had heard the claims from a number of people.
Another one of Leonne's friends said: "She was just absolutely sound, always up for a laugh. She was one of the funniest people I've ever met - she was lovely.
South Yorkshire Police placed a cordon around the area after the girl's body was spotted on a pathway in the residential area of Lordens Hill.
Temporary Superintendent Sarah Poolman told a news conference this evening that the girl had been reported missing 20 minutes before she was found.
She said police were treating the death as suspicious due to "concerns around the state of the body and the injuries."
Family members and friends had appealed for help to find Leonne on social media before learning the tragic news.
Stunned friends paid tribute to the teen on Facebook after hearing of her death.
Rother Valley MP Kevin Barron tweeted shortly after the news broke: "I am incredibly sad to hear about the discovery of a teenage girl’s body in Dinnington near my constituency office this morning.
"I would like to send my condolences to the family and friends of this young girl.
We must now allow the police time to investigate."