The idea was mooted in an informal council survey as officials look to update existing legal orders tackling dog fouling and anti-social behaviour.
A council report has backed the idea for dogs to be kept on leads near park visitor centres, but not a wider area.
People in breach of public orders can face fixed penalty fines.
Dog exclusion zones already exist on marked sports pitches and play areas in Wrexham, apart from owners with assistance dogs.
Extending the order to pavements and some parkland could cost an additional £20,000 in signage costs, according to the report.
A scrutiny committee meeting at the Guildhall on Wednesday agreed to allow a formal consultation to take place to push ideas forward.
Dog owners could be required to put pets on leads in country parks and on pavements under new public order plans being drawn up in Wrexham.