The hooker is set to captain Ireland for the upcoming autumn internationals and next year's Six Nations, before Schmidt reassesses his plans next summer ahead of the 2019 World Cup.
Best will be 37 when the tournament starts in Japan in two years time but he looks set to continue to add to his 104 caps.
John Hayes was the last Ireland player to be capped at that age but Best insists he will take each game at a time as he tries to thank Schmidt for his show of faith.
"If Joe had wanted to make a change of captain, he would have made the change," Best told Sky Sports.
"But he said early enough in one of the summer camps that as long as I was happy to continue, that I would be captain again, and then we'd reassess at the end of the season, on where we were, what's going on, and how I felt.
"I suppose that's probably something for the end of the season but it was nice to be asked again. When you're in that position you never like to assume anything, so it was good when Joe said they'd like me to do it again for the season.
"It gave me the confidence that he liked what I was doing, that he felt I was doing a good job."