A murder investigation is underway after the body of a man was found on Manor Fields Park, off City Road, in the early hours of May 12.
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.
Now, several Italian news outlets have reported the alleged murder victim is 34-year-old Carlo Giannini.
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.”
South Yorkshire Police declined to comment on the matter.
Police were called to the park at 5am on May 12, leading to the area being cordoned off to the public for all of Thursday.
By 2pm, South Yorkshire Police confirmed it had launched a murder investigation over the death.
Unusually, in their statement at 2pm, police said they were still trying to identify the victim.
A spokesperson for South Yorkshire Police said: “Anyone with information which could assist with our enquiries, who may have seen or heard any suspicious activity around the park between last night (Wednesday 11 May) and this morning, or who may have CCTV footage which captured any helpful footage, is asked to call 101, quoting incident number 122 of 12 May.
"Alternatively, contact Crimestoppers via their website Crimestoppers-uk.org or 0800 555 111.”