Definition
If something is at/in the back of your mind, it means that you are aware of it as a possibility or intention, though you are not actively focusing on it at the moment.
I've had the idea of learning to drive at the back of my mind, but haven't had time to sign up for lessons yet.
Starting his own business has been at the back of his mind for a while, but he hasn't found the right opportunity yet.
She has a vague idea at the back of her mind that she'd like to move to the countryside.