Strachan was on Tuesday appointed as successor to Craig Levein and has been given the brief of qualifying for the finals of a major tournament.
In-form Norwich winger Snodgrass is excited by the future with Scotland and is desperate to work and improve under his country's new boss.
He told the Daily Record: "I think Gordon can make me a better player. He made his name as a winger for Aberdeen, Manchester United, Leeds and Scotland - so I'm sure he'll feel he can improve my game.
"You learn different bits from every manager and that can take you a long way in your career. I'm looking forward to it.
"He'll want hungry players and I'll need to push myself hard to make sure I'm part of his plans. Hopefully he'll pick me, I'd love to be part of his plans for Scotland.
"In the meantime, though, I'll need to do the best I possibly can for Norwich.
"That means creating goals and putting the ball in the net myself. If I get the chance under him, I'll need to take it."