Melissa is convinced her puppy Nelly was stolen after noticing a bin had been moved, leaving a three-finger gap in the fence last Saturday.
Melissa said she "can't stop worrying" about Nelly.
She said: "The only gap that she could have got through was only about three fingers wide.
"I shared about her being missing on Facebook and then the woman sent my mum the message.
"I'm unsure as to whether it was a false account.
"She just sent that one message and then nothing was going through. She deleted her account and we couldn't get in touch so we rang the police again.
"We had only had her for about a week and I can't stop worrying about her."
Melissa added: "We found out that she was not in the house on Saturday just before 12pm.
"I rang the police and they said we had no evidence about her being stolen, so it couldn't be reported.
"I went around and checked my estate and everywhere."
A Greater Manchester Police spokesperson said enquiries into the missing pup are ongoing.
In a statement, a spokesperson said: "At around 2.30pm on Saturday 21 November 2020, police were called to reports that a puppy had been stolen from a garden on Marlborough Street in Ashton-Under-Lyne.
"No arrests have been made and enquiries are ongoing."
They are appealing for anyone with information to get in touch.
The RSPCA said the situation sounds "very distressing" for Melissa and Nelly and asked UK pet-owners to take extra precautions to protect their dogs.
They recommend getting pets neutered and microchipped as soon as possible, as well as buying a collar with contact details.