Police today released a photo of his injuries, which included several cuts to his face and a fractured cheekbone.
Detective Matt Campbell said police had identified a couple of suspects who they were looking to speak to shortly.
"The response from the public has been outstanding,'' he told APNZ.
"We've just been out conducting an area canvas up in Waikanae, and through that we've been able to identify a couple of potential suspects. So things are going good and we hope to have a result by the end of the day.''
Mr Campbell earlier said the suspect needed to come forward and be held accountable.
"Whether or not he describes it as a simple push does not detract from the fact that an elderly gentleman has suffered serious injuries as a result of a foolish act,'' he said.
"This assault on an elderly resident protecting the sanctity of his home is a cowardly attack on a helpless frail old man.''
Police said the youth wanted in connection with the shove was a European aged about 18. He was wearing a black top, black three quarter length shorts and a black baseball cap.