The force declared that to date no staff have made a request to wear the Islamic clothing.
But Detective Chief Constable Nick Baker said if any member did ask to where a burka it would have to be considered in line with force policies.
It comes after West Midlands Police's chief constable David Thompson opened the door to the move.
However, the West Midlands Police and Crime Commissioner has suggested it would be impractical for Muslim women police officers to wear a burka on the beat.
David Jamieson said the burka was 'probably not the best form of uniform' for bobbies and called for 'an outbreak of common sense' over the issue.
It comes after the force's chief constable David Thompson prompted international debate after he told the Express & Star that West Midlands Police would consider allowing officers to wear full face veils if such a request was made.
Staffordshire Police has become the latest force to say it would look at the possibility of allowing applicants or current employees to wear the the Islamic robes, which cover the body from head to toe.
Asked if he would be happy to see a WPc in the West Midlands wearing a full face veil, Mr Jamieson said: "For operational efficiency, if an officer had to handcuff somebody, or wrestle them to the ground, I think any sensible person would think that a burka was probably not the best form of uniform."
He said the burka had not come up in any job applications the force had received.
"I think we need an outbreak of common sense," he said. "Of 7,000 uniformed officers in the West Midlands, a tiny number of them are Muslim women. Nobody has made a request to wear a burka, and of all the people that are coming in – and we are looking to get a more diverse police force – nobody has suggested at all that a burka should be worn."
Mr Jamieson has called on Home Secretary Amber Rudd to run a consultation in a bid to offer guidance to forces on appropriate police uniforms.
"Of course it is up to every individual force to make the decision, but Home Office guidance would be extremely helpful," he added.
DCC Nick Baker, of Staffordshire Police, said: "We have an ongoing recruitment drive at the moment and to date we have had no requests to wear burka or hijab. However, if an applicant, or an existing employee did make a request, it would be considered against existing force policies."
Mr Thompson's comments have been criticised by the Muslim Association of Britain (MAB), who said wearing a burka would 'restrict duties'.
MAB spokesman Omer Elhamdoon, said: "I think what might be more productive is to do some sort of study as to why BME are not joining the police. We do not think the burka is the reason people are not joining."