As previously stated, your best chance to match the traditional way is as a US senior. With that being said, I have seen a few people backdoor their way into a program. By that I mean, they were in the regular pool of applicants as an intern, then a spot opened up someplace for the next year (so regular applicants were not eligible because they still had to do internship), so they pulled out of the match and took the spot. Should you expect this to happen? No. But some people get lucky.
In this scenario, if you were doing a pre-residency fellowship, then you couldn't snag that spot while as an intern you potentially could.