Isabelle Sanders, 51, was stabbed at her house in the Crookston area of Glasgow at around 1.55am yesterday. Her 85-year-old partner Norman Busby was also seriously injured in the attack and remains in hospital.
Police now believe the description of a man who was involved in an attempted armed robbery of a car at a Spar two-and-a-half hours earlier just 700 yards from the Raeswood Drive property matches that of Ms Sanders's killer.
The 33-year-old driver was injured as the man tried to steal his BMW car at around 11.15pm before running towards Househill Park.
Speaking at the scene, Detective Superintendent Jim Kerr said: "As a result of the support from the public and information passed, I would like to reassure the community that we are following a definite line of inquiry in relation to the murder of Isabelle Sanders and the attempted murder of Norman Busby.
"We now believe that the tragic events at Raeswood Drive may well be linked to an incident which occurred around two-and-a-half hours earlier."
Det Supt Kerr thanked the community for their support with the investigation but appealed for the drivers of particular vehicles to come forward, including a private hire taxi which was in Raeswood Drive at the time and any drivers on Crookston Road at around 1.50am. Anyone who saw a man running across the road was urged to contact police.
He said: "Please do not assume that we already know what you know, or that someone else has come forward with the information you have."