L1 to H1b in January?

If I am on an L1A visa and am looking to move companies is there a possibility of moving to a new company (if they are willing to sponsor me on H1B) in January 2015? My L1A visa is valid for 3 years in case this piece of information matters.

Any suggestions on what are the possible ways to make this move? Or does it mean I can move to the new company only in October 2015?