The 25-year-old man was walking with a friend when he was attacked in the High Street around midnight.
He suffered a bad head injury in the assault and is in a serious condition at the Southern General Hospital.
Enquiries so far have revealed that a woman was in the area around the time of the incident and officers are very keen to speak to her.
She is described as white, possibly in her 40s, with long shoulder length hair. She was wearing a knee-length red dress.
Officers are appealing to this woman to get in touch as she may have significant information which could assist the investigation.
Officers are continuing to carry out door-to-door enquiries and gather CCTV images in an effort to identify the suspect, who is described as being in his mid 20s; around 5 ft 10 inches tall with short brown hair, thin to medium build. He was wearing casual clothing, a t-shirt and possibly jeans.
Detective Sergeant James Quinn said: “We have still to establish a motive for this attack. A young man has been left seriously injured and it’s imperative we trace the person responsible. We understand there was a woman, wearing a red dress, who was in the vicinity and I am making a direct appeal to that person to contact us.
“It’s possible she saw something which could assist our investigation and help us trace the person responsible for this attack.”
Anyone with information or knowledge is asked to contact officers at Wishaw CID on 01698 202 600 or the police non-emergency number, 101. Alternatively, they can call Crimestoppers on 0800 555 111 where information can be given anonymously.