Jane Wilson, 42, was killed when she was hit by a red Ford Fiesta at around 1am on December 16 on the A6 near Kegworth.
Officers there have been conducting enquiries to find her family but have so far been unsuccessful.
Ms Wilson was born in Leeds and previously lived in the city.
It is thought she may still have relatives in the area or in London, where she also has connections.
Detective Sergeant Gary Haines, of Leicestershire Police's serious collision investigation unit, said: "We are desperate to try and find Jane’s family. She had no fixed home address and no family in Leicestershire, so we are now searching further afield to try and trace her next of kin.
"If you knew her, know her family, or think you could have information which will help us trace her relatives, please call us on 101 and ask for Leicestershire Police, and for DS 662 Gary Haines."