Hospital Chiefs want to change the law so that anyone caught smoking outside the Queens Medical Centre will be prosecuted.
.Staff at the hospital can currently ask the public not to smoke but cannot take legal action against them.
The Nottingham University NHS Trust wants to change a by-law to make it illegal to smoke on the premises. This means that staff will also have to leave the grounds when nipping out for a smoke.
Councillor Alex Norris, portfolio holder for Health at Nottingham City Council, believes this ban is long overdue.