Best has backed the Ireland coach to guide the Lions to a Test series victory in South Africa should he seek out the challenge.
Schmidt, 53, announced in November that he plans to finish coaching after the 2019 World Cup to focus on his family.
"The Lions is one of the few things he hasn't done," said Best.
"He hasn't been given the opportunity to be successful there."
Schmidt refused to rule out a return to coaching after taking a break and could well command a New Zealand coaching post if he does come back into the game.