A murder investigation was launched after the body of a man was found on Manor Fields Park, off City Road, in the early hours of Thursday, May 12.
The park remains sealed off tonight (Saturday, May 13) as detectives continue to investigate the circumstances around the man’s death.
South Yorkshire Police have repeatedly stated they are yet to formally identify the man after they were called to the scene at 5am on Thursday.
The young Italian national is reportedly from the Mesagne district of the city of Brindisi.
A source told The Star Mr Giannini worked at a pizzeria in Broomhill.
Several outlets report that Mr Giannini’s family are speaking with the Italian consulate to travel to Sheffield to help police with enquiries.
Outlet Today Cronaca reported: “According to what ANSA [Agenzia Nazionale Stampa Associata, a new agency] learned from Italian investigative sources, Giannini's relatives are in contact with the Italian consulate and it is not excluded that they may travel to Sheffield in the next few hours.
"According to reports from Brindisi, the 34-year-old left Mesagne years ago to move to Northern Europe to work in some restaurants. Two years ago he had opened a pizzeria in Germany.”
Anyone with information, or who may have seen suspicious activity in the park between the evening of Wednesday, May 11 and the morning of Thursday, May 12 is asked to call police on 101, quoting incident number 122 of May 12.