He was taken to A&E. MyLondon awaits a condition update. A local reported 'hearing a scream'.
There have been no arrests. A Met spokesperson said: "Police were called at 08:11hrs on Wednesday, October 15, to Mountsfield Park, Catford, following reports of a stabbing.
"Officers attended the scene alongside the London Ambulance Service who treated a man for stab wounds.
"He was taken to hospital where he remains, we await an update on his condition.
"A crime scene is in place at the location.
"At this early stage, no arrests have been made and enquiries are ongoing. If you have any information about the incident, please call police on 101 stating CAD1390/15Oct. Alternatively, you can call Crimestoppers on 0800 555 111 to remain anonymous."
A London Ambulance Service spokesperson said: "We were called at 8.06am today (October 15) to reports of a stabbing on Farley Mews, Catford. We sent resources to the scene, including an ambulance crew, a clinical team manager and a paramedic from our tactical response unit.
"We treated a man for injuries and took him to a major trauma centre."
Around five minutes from Mountsfield Park - on Rushey Green - a man was stabbed at around 3am. He was taken to hospital where he later died from his injuries.
There have been no arrests, and forensics continue to comb the scene for clues.