"We would like to reassure the community that this lady is safe and well."
An investigation was launched on May 25 following the aggravated burglary in Erdington when masked men broke into the house and threatened the occupants with weapons, possibly believing the girl was staying there.
Police said no one was injured in the incident.
"We are conducting inquiries into the motive for this attack," the spokesman said.
"We are not ruling the possibility this may be linked to a report received concerning the whereabouts of an 18-year-old female from West Bromwich, who was reported missing by her family."
He added: "Her family are clearly concerned about her welfare as are the wider communities.."
A spokesman for Birmingham City Council said: "We are working closely with the police to deal with a number of sensitive issues being raised by members of the community and will be working together with other interested parties to consider the wider and longer term implications for the city."
