The actress, who has had roles in both Emmerdale and Hollyoaks, is preparing to move to Australia after her footballer husband Harry Kewell was signed to Melbourne Victory.
"We heard a few months ago that she would love to have a role on Neighbours, but there has been no contact from her agent as yet," a show spokesman told the Herald Sun.
"If we could find a role for her that would be appropriate, we would, of course, consider her for the role. Our UK audience is massive, so to have somebody like Sheree would be great as she would be instantly recognisable to viewers over there.
"I suspect she grew up watching Neighbours in the UK, so I'm sure she would be open to the idea of joining the cast."
Murphy recently announced that she is expecting her fourth child with Kewell.