It's been my experience that oftentimes when a shelter posts a cute young dog on Petfinder they know that the dog is adoptable and know that they will not have trouble placing it. If that's not the case, then they post that there is a put to sleep date. Judging by the picture and the description of this dog I would guess that they plan to place him themselves. They say "this is just one of the many dogs ...". A lot of shelters will post a picture of one of their cuties, knowing that the dog is highly adoptable, already spoken for, or even already adopted. They do this to entice people to the shelter so that even if this dog has already been adopted the people coming to visit might just fall in love with and adopt one of the other needy dogs.
Your best approach is to call the shelter, inquire about availability, ask if there is a put to sleep date, and, if so, ask if they would be willing to place the dog with a rescue group. BUT before you ask about their willingness to place the dog with a rescue group please make sure that you have the commitment of a rescue group to take the dog.