Having close and fruitful relationships with other people in which they share their intimate thoughts can be endearing. Yet remember that coaching is a professional relationship, just as doctors, accountants and lawyers have with their clients. Your responsibility is to work ethically within professional boundaries.
Here's a health warning. Beware of falling in love and expecting to run off with a client to a long and happy life together! While it's impossible to say that coach-client personal relationships never succeed, switching from coach to lover rarely leads to satisfactory long-term results.
Of course, you can become friends with your client after the coaching contract is complete. For coaching to be successful, gently tell clients that you're not going to become great buddies with them while coaching them.
Coaching is a lop-sided relationship in which clients open the box on their vulnerabilities. Meanwhile, the coach's own life and issues are kept private. Re-balancing that history and redesigning the relationship involves close self-scrutiny, which is very difficult to achieve in the face of an established pattern and history between two individuals.