Kelly Clarkson Says Stranger's Showing Up at Her Home, Files Police Report

Kelly Clarkson says a strange person is showing up to her house, trespassing on her property and leaving her unwanted gifts ... so, now she's getting the police involved.

Law enforcement sources tell TMZ ... for the past month, the same person's been popping up at Kelly's L.A. area home, going up to her porch and dropping things off for her.

We're told they're leaving behind cards, plants and other random items for Kelly ... even though she told cops she's never met them before, and doesn't know who the stranger is.

Our sources say Kelly has yet to come face-to-face with the intruder, but we're told her security was concerned enough to call LAPD to file a report ... and now LAPD Threat Management is investigating.

Cops see the person's alleged behavior as very troubling -- they don't know yet if it's a fan who means no harm, or a situation that could escalate into something far more sinister.

Our sources say Kelly's got surveillance footage of the person dropping stuff off on her porch ... and LAPD is trying to identify them for a background check, and to assess potential threats.