The Monster's Ball star has been romantically involved with make-up artist Connie Angland for almost 10 years, but unlike his last ex-wife Angelina Jolie, who is engaged to marry Brad Pitt, the actor doesn't want to walk down the aisle again.
He tells CNN newsman Piers Morgan, "I told her, 'Look, when you think of it this way, this is my longest relationship and we're not married.' So it's not real hard to figure out!
"Plus, you know, if you do that then the press would get into that, and call her number six or something like that and that's not fun. We're doing just fine the way we are and we have a beautiful seven-year-old daughter. It's all fine so let's leave well enough alone, you know?"
Thornton has five failed marriages behind him, including unions with Playboy model Pietra Dawn Cherniak and actresses Toni Lawrence and Cynda Williams.