January is perfect. You can start them inside and by spring they should be ready to go outside in pots.

Not sure where you are located? In my area in January the fig would be frozen and branches probably dead.

Maybe in your area not so bad but still check that you are not taking branches that are damaged or dead. Healthy and pencil size is best and the cambium should be a bright green.

Ooops. My bad. I just assumed they would be started indoors, and I shouldn't have. That said, if they are to be started indoors in a well heated location, starting in Jan is good. On the other hand if they are to be kept outside starting in Jan wouldn't work unless you are in truly tropical location.