Proposals to update existing dog control orders would see the list of places where they are in force expanded.
The council has launched a one-month consultation on the proposals.
Under existing dog control orders, dogs, apart from guide dogs, are excluded from children’s play areas, remembrance gardens, some school grounds and wildlife gardens. Leads must be used on footpaths, cemeteries and some ornamental gardens.
Councillor Mark Dobson said: "We introduced dog control orders two years ago to clamp down on nuisance and dangerous behaviour. The rules are very effective in encouraging responsible dog ownership."
Reviewing the orders would ensure they remained appropriate, he said. They would give dog owners clarity on responsible ownership.
Owners in breach of an order can be fined £75 or £1,000 if prosecuted. Almost 120 people were fined last year.