If you don't have a firm job lined up, with a specific departure date I don't think it is unreasonable for you to go to re-current. Then you can continue to do the job they need you to do until you are ready to let them know you are leaving.
On the other hand, I know my boss would not hold it against me if I told him I was exploring other options so I'd feel free to let him know my concern that I wanted to be fair to the company. He'd appreciate the openness and maybe even have a discussion of whether there was anything he could do to make we want to stay.
If you don't have that kind of relationship and you think you'd be punished for looking even if you decide to stay, then better to not say anything until you are ready to give notice.
My $.02 but there are so many variables we don't know about your history with the company that it is hard to give a simple answer.