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No, unless you are giving notice.
Your current boss would probably have reservations that may include not wanting you to leave the firm, or what if the two of you do not see eye to eye? Or you could be under the illusion that the both of you have built a strong bond that may make it feasible for you to tell your boss.
Whatever the reason i'm of the opinion that it would be premature especially if you have not found the job yet. One never knows how people react to different pieces of information.
