Casey Anthony's Parent Want To Meet With Rascal Flatts

TMZ has learned ... George and Cindy Anthony reached out to the band's reps this week after hearing the song, "She's Going Places" -- which lead singer Gary LeVox co-wrote with another singer named Cledus T. Judd.

But the band isn't exactly in a hurry to respond -- a rep for Rascal Flatts tells us the band is mulling it over and has yet to decide if they'll meet up with the Anthonys.