A true elder brother in the parable of the prodigal son?

The Prodigal God: Recovering the Heart of the Christian Faith

by Timothy Keller

We are using this book in our Covenant Group bible study, studying the Prodigal Son parable in Luke 15:11-32. This book by a Timothy Keller is quite good but there is one interpretation of this passage we have not encountered before. 

In my previous studies, I remember moving from a focus on the younger son to the elder son, a focus on the homecoming of the wayward to the selfish and unforgiving elder brother. 

But Keller brings it even further. He posits a view that in this parable, there is an implied lesson on Jesus being the true elder brother, someone who woulf go all out to search and bring back the younger brother back to the father, back to the family. 

While it is not unreasonable to have such a reading of the passage, can we go that way in proper exegesis of the passage?

I want to try to get to the bottom of this. 

pearlie