The New South Wales government has approved similar legislation.
The WA Police Minister Rob Johnson says he will be discussing the possibility of legislative changes with the Police Commissioner Karl O'Callaghan today.
"I'm concerned at the idea of police not having the power to request drivers to remove helmets or other face coverings for ID purposes at the roadside," he said.
"So, I will also be looking closely at the New South Wales legislation to see exactly what they've done."
Mr Johnson says officers need to be able to identify motorists.
But, he says it would be done with sensitivity.
"I'm certain that we would try and ensure some sensitivity in relation to anybody that for religious reasons or any other reasons would find it difficult to remove their head gear or clothing or helmets that cover their heads and particularly their faces," he said.
The Police Commissioner has already said that state laws covering burqas, motorcycle helmets and other face coverings need to be changed.
Under current legislation, police are not able to ask people wearing full face coverings to remove them.
Mr O'Callaghan said the Traffic Act needs to be amended.
"You ought to be able to satisfy yourself that the person driving the car, or a motorcyle, is the person on the driver's licence," he said.
"I am going to push for that legislation that will include any sort of face cover."
The Islamic Council of New South Wales said it accepted the decision
"If you're asked to do something by a police officer and it's legitimate, then you do it," council chairman Khaled Sukkarieh said.
The Muslim Women's Association said it would prefer that a female police officer was on hand when the veils were removed and if that happened then "nobody could really complain".
The Police Association of NSW welcomed the move, saying it was a loophole that had to be closed.
"It will provide clarity and certainty for both the public and for police officers," the union's acting president Pat Gooley said in a statement.