The city council said it wanted to “de-normalise” smoking by barring it and using existing laws to step up controls on tobacco.
The authority said about 17% of residents were smokers who average £2,500-a-year spent on the lethal habit.
There are no smoke-free UK cities but Bristol is tipped to be first as it is piloting smoke-free public spaces.
Liverpool said: “The council wants a smoke-free city allowing all its communities to live longer, healthier and wealthier where they can play and work without exposure to the harms
of tobacco smoke.
“In addition to causing avoidable illness smoking creates a greater burden for the most disadvantaged.”