But no statement included a conversation the 75-year-old now says he had with the foster grandmother shortly after a neighbour alerted him William was missing.
Mr Savage says the 30-second chat outside the woman's home involved her telling him William's foster mother had gone in to make or have a cup of coffee and then noticed the boy wasn't there.
"I'm pretty sure that's what she said," Mr Savage told the inquest.
"That must have been something that I remembered. It might not be right."
Pressed on how strong his recollection was, he said: "I still think that happened but I can't guarantee it. I'm not going to guarantee something I'm not sure about it."
After scouring the bush for up to 45 minutes on a path that took him to his backyard, Mr Savage did not inform anyone his search had found nothing, the inquest was told.
"I walked out the front just to see what was happening and then I went back inside," he said.
"I see the police (were) already there. I thought, 'that's the police, they don't need me'."
He said he made himself some food and tea because he thought whether he spent the day searching or making the long drive to see his brother in Casino he "should do it on a full stomach".
Neighbour's conversation with grandma after William Tyrrell's disappearance
