The body was found on Monday morning at the site on Oxford Road which is being transformed into student accommodation by Wates under a £60m deal.
Police have confirmed the body was of a 19-yeat-old University of Manchester student who went missing after attending a ball at a hotel near the site on Saturday night.
A Wates spokesperson said: “We can confirm that there has been an incident involving a member of the public on our site on Oxford Road in Manchester and our thoughts are with the family at this time.
“We are cooperating fully with the authorities to establish the circumstances which led to the incident.”