This is exactly what I've done in the past. I haven't had any issue. I don't make a big deal out of it, but I do let them know I'm currently happy where I am

This is exactly what I've done in the past. I haven't had any issue. I don't make a big deal out of it, but I do let them know I'm currently happy where I am so, if they decide they are interested in moving forward, they'll have to make it worth my while.