Jack Barnes, 29, died in 2016 after suffering a heart attack during the restraint, where he was held down by four men - working for an external company - at the station as security.
Footage taken from body cameras showed that the men chased Mr Barnes for nine minutes through the station after an altercation. He was restrained face down and was heard saying he could not breathe seven times in the footage.
Father-of-one Mr Barnes suffered a heart attack, followed by a cardiac arrest and died in hospital seven weeks later. An inquest into his death last Friday, was told that restraint was continued for two minutes after Mr Barnes was last seen moving without any attempt at CPR.
The inquest ruled Mr Barnes was unlawfully killed.
Having been approached by Mr Barnes' family, Hull East MP Karl Turner has now written to the Director of Public Prosecutions Max Hill QC, to request a review of prosecutions in light of coroner Nigel Meadows' findings.
In the letter, Mr Turner said: I am writing to you on behalf of my constituents, the family of Mr Jack Barnes, regarding Manchester Coroner’s Court’s recent ruling that he was unlawfully killed in 2016.
"Thank you for your consideration of this matter and I look forward to your reply."
Recording a verdict of unlawful killing, senior Manchester coroner Nigel Meadows said the men became “carried away by the bravado of the chase.”
He said that grossly excessive and unreasonable amounts of excessive force were used to restrain Mr Barnes, including pressure on his neck.
Mr Barnes’ mother Patricia Gerrard said: "How can anybody justify ignoring somebody’s repeated pleas to be allowed to breathe? It is absolutely appalling and the actions of these men are the reason Jack is no longer here and no longer able to see his little girl, who was just three-years-old when he died. I hold them all responsible. Jack was a very loving boy and so deserving of life."
A spokesperson for Greater Manchester Police said: "Greater Manchester Police conducted a full investigation into this incredibly tragic case and arrested four men in relation to the incident. Following a review by the Crown Prosecution Service, all four men were released without charge. Our thoughts remain with Jack's family and loved ones at this time."
Mrs Gerrard was represented by solicitor Lauren Dale, of Hudgell Solicitors, and barrister Frederick Powell, of Doughty Street Chambers, at the inquest.
Ms Dale said: "This case is a reminder of the tragic consequences of security and other personnel seeking confrontation and using excessive force."