PC Jamieson said the force was conducting house to house enquiries and looking at CCTV and dashcam footage.
“So far, these enquiries have proven negative for locating the woman or driver, and we are now in a position of needing to appeal for the wider public’s help,” she added.
The woman is described as being white and wearing dark coloured leggings and Ugg boots, while the driver is a white man who was wearing a black coat or jumper.
The vehicle, which is described as a dark coloured hatchback car, was last seen heading towards Davenport Train Station just after 06:30 GMT on Saturday.
A force spokesperson said the vehicle could well be outside Greater Manchester and so they were appealing for anyone in neighbouring regions who may have information to get in touch.
