Han is so intrinsically linked to the Millennium Falcon that its difficult to picture it ever belonging to anyone else; its his ship. Except, of course, it wasnt always that way.
It is revealed in The Empire Strikes Back, in an exchange between Han and Lando, that he actually won it (fair and square) from his old friend a long time ago.
The film should explore how the two smugglers became good friends - probably with a lot of womanising involved - and show just how Han managed to win the ship. In the now discarded EU it was a Sabacc (a popular card game across the galaxy) tournament on Cloud City, and if the movie followed a similar path then we could be in for some Casino Royale-esque card playing. And youd imagine that the way Han wins wouldn't actually be fair or square.