The city already has six such parks and three under construction but will need 10 more to meet the Denver recreation department's recommendation, The Denver Post reported Friday.
The plan is likely to create a major battle between dog owners and those who want parks reserved solely for human use, the newspaper said.
City officials are gearing up for that tussle.
"Even though there is strong demand," City Council President Jeanne Robb said, "other people don't want to take park land already committed to other uses, passive or active, and give up that turf."
Denver has one dog park for every 100,000 residents, which puts it behind other major cities. Portland, Ore., leads with almost six parks for every 100,000 residents, the Post reported.