The body of Charlie Saywell, 25, was recovered from the River Medway near Chatham, Kent, on Tuesday morning.
On Monday evening, Charlie went out with friends before taking a taxi to his home in Brompton.
But officers believe instead of heading home immediately, he went for a walk into Chatham town centre between 12.10am and 2.40am.
Kent Police said the 25-year-old may have “mistakenly” got into an unidentified car.
It is inside that car where he was reportedly “assaulted by the driver and suffered facial injuries”, police added.
Detective Sergeant Karen Caulfield added: “While we do not have specific information about where Charlie went between 12.10am and 2.40am…
“He had a phone conversation before his death which indicated he may have suffered an assault in the town during that period.
“We are appealing to anyone who may have seen Charlie walking in the Gillingham and Chatham areas during these times.
“We are particularly keen to hear from anybody who saw him in a fast-food outlet or involved in an altercation in or near to a car.”
Charlie’s mum, Victoria Brown, also issued a plea for information, saying: “If you have witnessed my son Charlie’s movement during the early hours of that morning and can offer any information, however small, please can you contact Kent Police so our family can have some answers about what happened to him.”