Your resume or CV probably indicates your current location. Usually, this is either by listing your current position or your current university. If the job ad doesn't specify that they require local candidates (or candidates who are already currently legally employable in that country), then I think that the location listed in your resume is sufficient when you are applying for a position. If your location is a concern for the company, the recruiter (or hiring manager, if there isn't a recruiter involved) will ask you about it.
For me as someone who conducts interviews, anything that is related to immigration is handled through Human Resources. If you ask me about it during a telephone interview or an in-person interview, I won't be able to answer any questions about it, and I'll refer you to the recruiter who set up the interview. This isn't because I don't want to answer the question, but because I have no insight into the process.
Note: my answer is based on my experience in being involved with hiring for a couple of large US employers in the software industry, although I do have some experience of being a candidate and getting hired in the UK and Australia as well. My conversations with my Australian employer gave me the impression that the process was similar enough. They've each said that it was quite clear from my resume that I'm an American citizen and they assumed when they got my resume that I would require a visa.