Asklemmy

It is possible to an extent with certain breeds, e.g. Egyptian Mau. However, they are curious and skittish so may not follow you everywhere if they find something interesting or get spooked. When you get too far from their known "territory" they may stop and wait for you to come back, (while also yelling at you to come back to the concern of passers-by!).

I used to go for walks with my gf and her egyptian maus. They would follow along like a pride of tiny lions but spread out a bit, so while we walked on paths their parallel routes would go through gardens, over roofs, fields, fences, etc.

In fact it was more of an effort to train them not to follow us everywhere, e.g. to the shops, work, etc. They would often follow neighbours' children to school and back (and sometimes follow the wrong child home and get lost!).

Maus are also more amenable to being on a leash than most breeds, although you need to get them used to it early in life.

The main problem is if they decide to run away from something they are blazingly fast and near impossible to catch and recover from whatever inaccessible perch or hidey-hole they run to. My gf's cats had been trained to return to the sound of jangling keys, but that only worked most of the time.