Just looking to grow my podcast, we just ask the athletes or coaches to give us their journey story. So nothing too demanding.
Ask them! If you don't have any similar interviews yet, get some done in a niche close to this one. Credibility is important, and if you show you've done some and they listen to just part of one interview, that can be what pushes them over the edge.
Everyone likes to talk about themselves. So don't be afraid to make the connection. I work with a local pro soccer team and it was easy to connect with a senior management team member. From there, the players are all accessible. They're just regular guys, running around and wanting to have a good time. You could find the marketing director and ask who's the best talker of the bunch.
Be sure to let them know they get to use the content as well. The teams are looking for reasons to be in the news. You're giving them one. Something they can share on their Facebook page, or in an email to their fans, that helps their followers feel closer to the team, is valuable. Don't get stuck thinking you're trying to "get" something from them. You're giving something, too.