It looks like soon we will be able to walk with a pokémon, the same way we walk our eggs, but the reward will be candy!

Pokemon Buddy System has been data mined! - Pokemon GO Hub

Pokemon GO Buddy system has been data mined from the latest app version. We will be taking our favorite Pokemon for a walk soon. The Buddy system was first seen on AeonLucid's PogoProtos , the biggest Github repository for analysing Pokemon GO network traffic. The Buddy system was introduced in the code base in 0.35.0 update.

pokemongohub.net