The con artists call from a withheld number, stating they are calling from a local vets in possession of the lost pet.
They then tell the owner their pet has been involved in an accident and requires emergency surgery, and in order to proceed, they require payment.
A post in a community group which shares information for people in the West Midlands claims that those who run the group have been made aware of the scam.
The RSPCA has also been alerted to multiple reports of similar scams and has moved to issue advice.
A spokesperson for the RSPCA said: “We are disgusted by reports that scammers are preying on upset people who have lost their pets.
“We would urge anyone who is contacted and asked for money in this way not to give out their personal details and to speak to police.”
The Express & Star contacted local veterinary Vets4Pets in Reedswood, Walsall, to gain a better understanding of what a veterinary practice would do in a situation like the one presented by scammers.
A spokesperson for the practice said: “If somebody brought in a pet which was injured the first thing we would do is check for a microchip.
“We would then call the number connected with this and ask them if they were missing a pet.
“If they said yes, we would ask them to come in to confirm it is theirs, and we would ask to see photographs to make sure of this.
“We would never ask for a payment over the phone in a situation like that.”
Over in Shrewsbury, con artists have been carrying out similar attempted scams.
The scammers posed as members of staff from Medivet in Sutton Farm, telling owners to give bank details over the phone to get their pets back.
A spokesman for the practice said: “We have been made aware that owners of missing pets have been receiving phone calls from people posing as members of staff from Medivet Sutton Farm.
“These scammers tell the pet owners that their missing pet has been found and is at our vets, and in order to get their pet back, they must give their bank details over the phone to pay.
“This is a scam. We would not ask for money for a service such as this.
“If you receive any similar phone calls and want to check their legitimacy, please call the practice on 01743 352274.”