Interstellar FTL travel might be possible if you could shrink things really, really small like elementary particles small and then shoot them through a mini wormhole and then have them somehow reconstruct on the other side? If you wanted to get back up to macrosize, that shouldn't be a huge problem as your micro-particles would look for some kind of planet and then start upscaling itself. Eventually, you'd be able to recreate "yourself" on the other side assuming that you had all the necessary ingredients.
DNA probably isn't small enough to do the traveling bit, but it certainly fits the bill for the self-recreation bit.
The actual FTL part would be extremely quick but the wandering through space until you hit a planet that has the necessary elements could be mindbogglingly or improbably long. However, once it did happen, it should only take a couple million to billion years to recreate "yourself."
The main problem with this idea isn't whether it's possible -- it probably is (we just can't find, let alone "aim", mini wormholes). The main problem is what do you consider "you?" If we mean a bit by bit copy -- this obviously isn't it. But if you have a much bigger version of what you is -- this certainly fits the bill.