Police are now likely to focus on hotspots like the Norris Green and Croxteth housing estates, Croxteth country park and Walton Hall park, where incidents have been reported.
Inspector Louise Harrison, of Merseyside police,said: "We have alot of genuine dog owners, but we have also seen an increase in the number of irresponsible owners.
"It tends to be predominantly young men using them as fashion accessories, and we are worried that some of these animals are bred especially for attacking and are being trained in a violent way.
"We want the public to tell us who owns these dogs - they know who is not being responsible with them. It will help us form a picture of the problem we have got."