Someone mentioned that Ortiz has a great deal of pride, and because of that, he might accept a minor league assignment in order to possibly regain a semblance of his old form. I agree that he probably has a lot of pride, but I actually think all that pride would prevent him from accepting a minor league assignment. Those feelings can work both ways. For example, at the beginning of 2005 Jason Giambi refused to accept a minor league assignment, probably because he felt it was beneath him. I think there is a good chance Ortiz feels the same way.
Obviously this is nothing but speculation, as I don't know what his mindset is. With that being said, I think the above is plausible, and probably likely.