Can I confront an employee about interviewing for another job?
What would you do if this employee admitted or denied the interview?
From my perspective, your best action is to acknowledge--to yourself--the emotional charge that this incident triggers. Do you feel betrayed? Abandoned? Dupped?
Now, put this emotion aside and focus on your next logical step. Start preparing for this employee's departure. You will get much more by staying quiet--and preparing--then you will by any confrontation.
Your employee has one foot out the door. Get ready for the move. How can you quietly get ready? Is it possible to promote cross training so that someone else knows this employee's job?
Often in life, we have much more power when we do not let someone else know what we are thinking or what we know.
Remember Don Corleone's famous line in The Godfather: "Never tell anyone outside the family what you are thinking again."