Curiosity is a characteristic of many successful mentors and mentees. Curious individuals proactively seek solutions to problems that they don't know the answer to. They also tend to be more motivated to find ways to improve their mentoring performance (e.g. research best practices, ask for advice from superiors).
Curiosity won't Kill You
It is commonly thought that curiosity is a good way to get yourself into trouble, but this isn't always the case. Several studies have shown that those with a curious mind tend to go further in their career - they always find a way to make things happen. Talk with your mentor today about how you can be more curious. You never know what will come of it!