A member of the public called emergency services after finding the man lying in Annette Street in the Govanhill area of Glasgow at around 7.05pm on Sunday September 29.
The 34-year-old man was taken to Queen Elizabeth University Hospital, where he was treated for lacerations to his thighs and his abdomen.
He has since been released.
Officers believe the man may have been attacked and are appealing for anyone who was in the area around that time to contact them.
CCTV footage shows several people around at the time though it does not show the man himself.
Police are keen to speak to anyone who was in the area early on Sunday evening and would like to trace a group of youths who were seen nearby.
A police spokesman said: "In particular, there is a group of youths near to where the man was found and officers are directly appealing to them to get in touch as they may have seen something which could assist the investigation and help officers establish what has happened to the man.
"Anyone with information is asked to call CID officers at Cathcart police station via 101, quoting incident number 3921 of 29 September.
"Alternatively, please call Crimestoppers on 0800 555 111 where information can be given anonymously."