Police were called at 11.35am on Friday (September 3) to Birchfield Road in Cheadle Heath, to a report of a stabbing.
Emergency services attended and enquiries established a man in his 40s had been stabbed.
He was taken to hospital but his injuries are not believed to be life threatening.
Police believe Allen Anthony Brown (aged 44), of no fixed abode, may be armed and have urged the public not to approach him.
He has connections to the Manchester and Stockport areas.
Anyone with information should contact police on 999 quoting 1127 of 03/09/21.
Alternatively details can be passed on via the LiveChat function at www.gmp.police.uk, via the independent charity Crimestoppers on 0800 555 111, or by calling 101.
