I am an F-1 international grad student. I am wondering if I can obtain an OPT one semester before graduation.

I am switching from an MS to a Masters of Engineering program, and that switch takes one semester to come into effect. Practically speaking though, I finish the "credit requirements" for the program this December, so I would not have to physically be present as of January 2014. My official graduation date however, would be one semester later, in May 2014. A company might be interested in hiring me as of January, so is there a way I could apply for the OPT now, in order to be able to start working as of January?