The incident took place in Abercromby Street in the east end of Glasgow on Thursday evening.
An 81-year-old man was on his way home from a nearby chip shop when he was approached by a man he did not know who then followed him.
The attacker managed to get inside the pensioner’s sheltered housing flat and then assaulted the man and his 80-year-old wife.
The man, who fled along Stevenson Street towards Tobago Street, is white, 6ft, aged in his mid to late-30s, of slim build and with dark hair which is distinctively receding at the top.
He was wearing a black jacket, blue jeans and glasses.
The elderly couple were taken to Glasgow Royal Infirmary where the woman is receiving treatment for facial injuries and a broken hip and the man for injuries to his face and hand. Both are in a stable condition.
Detective Sergeant Stephen McGrath said: “This was a cowardly and despicable assault on an elderly couple who would not have been able to communicate with their attacker.
“Officers are currently examining CCTV footage and conducting door-to-door inquiries, however we need the support of the local community to find whoever is responsible.
“At this time the motive for this crime is unclear however one line of inquiry is that it may have been an attempted robbery.
“From our inquiries so far we can see that prior to the incident, the suspect stopped to speak to a couple on Abercromby Street whilst he was in the company of the victim, and it is absolutely critical that we speak to them as soon as possible.”
Anyone with information can contact police on 101, or anonymously via Crimestoppers on 0800 555 111.