The best solution, and my recommendation, is to use a properly treated pole, filled with premixed concrete in a monolithic spill. Place a minimum of six (and better eight) inches of concrete below the column and eight or more inches above the post (this is known as the lower neck). To answer the question at hand, yes, you can build a new pole barn on top of existing concrete. However, just because it can be done doesn't mean it's the best option for you.
One of the forces that a pole building column must be able to withstand is lift, that is, the columns are literally blown off the ground by the wind. Not all wood treated with preservatives meets the requirements for pole barns established by the International Building Code. This revolutionary construction method is no different from conventional standards when it comes to determining whether to build a barn with posts on the current slab.