Police were called to the One Smithfield Square site on Monday afternoon after the body of a man in his 20s was discovered by a construction worker.
Police had earlier been called to a report of a naked man running through the streets of the Northern Quarter at about 10.30pm on the previous Friday.
They made a search of the area but couldn’t locate the man. It is believed he had climbed over a fence and entered the construction site.
Detective Inspector Brian Morley, based at North Manchester INPT, said: “This is a tragic case where a man has lost his life after apparently falling into a lift shaft and our thoughts are with his family at this time.
“Our work now is concentrating on the minutes leading up to his death. We are now confident that the deceased is the same man who was running naked round the Northern Quarter on Friday night.
“It was a normal busy Friday night and no doubt dozens of people must have seen this man. I have no doubt that if you saw him you would remember.
“We have spoken to a number of witnesses, both on the street and those who work in bars in the area, but I want to appeal to anyone who saw this man, and we have not yet spoken to you, to call us.
“We believe he may have got undressed near to the Adobe bar, and a bag containing a laptop, phone and a passport were found nearby.
“We are also investigating reports that he was seen at the Holiday Express and the Bluu bar before he climbed into the construction site.
“Our main message is simple – if you saw this man on Friday night then please call us. Your call could help us piece together exactly what happened.”
Anyone with information is asked to call police on 0161 856 3221.