Police believe they are closing in on an Oxford University employee and a US professor suspected of stabbing a 26-year-old man to death.
Chicago Police urged Somerville College senior treasury assistant Andrew Warren, 56, and Northwestern University microbiology professor Wyndham Lathem, 42, to give themselves up as they warned their search is "intensifying".
Officers said on Thursday that they believe they have an "idea of their whereabouts" after they fled Chicago where they are suspected of murdering former hair stylist Trenton Cornell-Duranleau in Lathem's apartment.
"Our primary focus is to facilitate a safe surrender and we strongly encourage Professor Lathem and Mr Warren to do the right thing," a force spokesman added.
The message came after Oxford University urged Warren, who oversaw pensions and payrolls at the college, to hand himself in.
"Andrew Warren's colleagues at Somerville College have now all been informed and are shocked to learn of the case," a spokesman said.
"Whatever the circumstances, we would urge him to contact the US authorities as soon as possible, in the best interests of everyone concerned."
A police report said the men "are to be considered armed and extremely dangerous" and were last seen getting into a grey 2007 Hyundai.
Police said they have placed restrictions on Warren's visa and Lathem's passport to prevent them leaving the country.
Officers say the victim, who lived in Chicago, was found with multiple stab wounds in the 10th floor apartment near the city centre at around 8.30pm on July 27 before being pronounced dead at the scene.
Court files give Warren's address as the Oxford college but he says on Facebook that he lives in Swindon, Wiltshire, and is a former cashier and driver for Stagecoach.
Lathem has worked at Northwestern since 2007 and specialises in the bacteria that caused the bubonic plague.
Northwestern University said he has been placed on leave and is banned from entering the campus.