Is there a specific word for the process where someone is trying to learn a specific piece of information from you?
Is there a specific word for the process where someone is trying to learn a specific piece of information in a conversation with you without revealing what he wants ?
This is a fishing expedition (or, in a small way, merely fishing):
A search or investigation undertaken with the hope, though not the stated purpose, of discovering information.
— Lexico by Oxford
It's also used in another, related context, of getting someone to offer you something you want. For example, if you mention that you're driving somewhere, someone else might fish for a lift.