Police have said they want to speak to a man seen running close to where Saudi student Nahid Almanea was killed.
The white man, aged between 18 and 25, of medium build and with dark hair was spotted to coming out of an alleyway which indirectly links to to the Salary Brook Trail, where the 31-year-old was stabbed.
He was wearing a long sleeved, plain hooded top that is described as London bus red and dark trousers.
Ms Almanea was stabbed 16 times while walking along a path on Tuesday morning.
Nadia Almanea was attacked on her way to universityIn a statement, Detective Chief Superintendent Steve Worron said police also wanted to hear from anyone who could help identify a man wanted for questioning over an attack on a woman in Peache Road, Colchester, at around 10pm on June 19.
"The location of this attack, and some aspects of it, including reports that a knife was seen and the victim was a woman, mean that this suspect is also of interest to the Almanea investigation," he said.
The attacker was described as white, in his early 20s, and around 5ft 7in to 5ft 8in tall. He was of medium build and had a narrow face, appeared unwell, and possibly had fair hair.
Police have been searching the area where Ms Almanea was stabbedMs Almanea had been taking an English language course at the University of Essex as part of her studies for a life sciences PhD.
Police released a CCTV picture of the 31-year-old taken moments before her death and a map of her likely route from the home she shared with her brother to the spot on the Salary Brook trail where her body was found.
Police have previously said the fact that Ms Almanea was stabbed multiple times bore "obvious similarities" to the murder of James Attfield, a vulnerable man with brain damage who was stabbed more than 100 times in a park in Colchester in March.
Police released a map showing Ms Almanea's routeIn the statement on Saturday, police said it was still not clear whether the two killings had been carried out by the same person.
"A criminal profiler from the National Crime Agency has carried out a thorough assessment of all the evidence in connection with both murders," Detective Chief Superintendent Worron said.
"A decision has been taken that they remain separate but parallel investigations at this time.
"However the circumstances of both crimes mean that we must consider the possibility that the same killer or killers are responsible."
James Attfield was stabbed more than 100 times in MarchPolice have urged people to remain vigilant and be careful about going out alone following the attacks.
Superintendent Steve Ditchburn said extra patrols were being carried out across the town.
"Our advice to people is that we have now had two knife murders in Colchester in less than three months where the motive for the attacks remains unknown," he said.
"Both of these attacks were on lone people who were in locations where it appears no one else was nearby at the time.
"For that reason we would remind people to take sensible precautions to stay safe. This includes avoiding any situations in which you could find yourself isolated and alone in a public area."
:: Anyone with information is asked to contact the Major Investigation Team on 01245 282103, Essex Police on 101 or contact Crimestoppers, anonymously, on 0800 555 111.