I am in the process of relocating (August) and looking for a job in the new city while employed.

Question: Obviously, as part of the process I’ll be doing a lot of talking on the phone, and I have an accent. I am a green card holder, and don’t want to put off prospective employers who may be concerned about having to deal with helping me get my paperwork straightened out with immigration (not an issue since I am a permanent resident). Would it be appropriate if I put my status on my resume so that they know from the getgo?