Yes, dogs can lick their paws. They do this all the time! Some people think it's because they're trying to clean them, but it's just because they're trying to soothe them. There is no denying that dogs have a keen sense of smell and can often detect things that humans cannot. It is common for cats to try to lick their paws when they smell something they don't like on them. It would also be possible for them to simply be attempting to get a taste of something they find interesting.