Mohamed Mussa, known to his friends as Mussa, a Dutch national living in Wandsworth, had been reported missing on Sunday, 17 October.
Enquiries are ongoing as to how he came to enter the river.
Detective Chief Inspector Jim Shirley, from the Met’s Specialist Crime Command, said: “Our last sighting of Mohamed is of him walking past Simmons bar on Putney High Street towards Putney Bridge at 5.29am on Sunday, 17 October.
“We are confident he did not turn left down Lower Richmond Road or cross over the road towards the church and cinema, but are not clear on his next steps and we are now asking for the public’s help in trying to ascertain exactly what happened.
“Were you on or heading towards Putney Bridge at around 05:30hrs that morning or driving on Putney High Street at a similar time? Please check any dashcam footage in case you captured anything that could help with our investigation and get in touch with us as soon as possible.”
Mohamed was walking alone and was wearing a navy trench coat, light blue shirt, dark trousers and canvas trainers, at the time of the last sighting.
Anyone with information is asked to call 101 or the incident room on 0208 721 4266.