It could be worth taking some slips off it and trying to get them to grow just in case the move doesn't work out too well or if the clippings take off, you won't need to worry about the original plant.
Found this [broken link removed] ( as I haven't tried clippings from white jasmine myself)
Q. A friend gave me jasmine and bougainvillea clippings. I put them in water and covered the lower part with plastic. What is the best way to get them to grow?
A. Many gardeners have better luck rooting cuttings directly in soil than they do rooting the cuttings in water. Prepare the cuttings by removing all foliage that would be under water or under the soil. Then, if you wish, add a bit of rooting hormone to the ends of the cuttings. (Rooting hormone should be available from your local garden center.) Remove any flowers and flower buds you see, then insert the cuttings into soil. Keep them out of direct sun and keep them well watered. After several weeks, they may root and begin to grow.
You may find more help on-line as to when is the best time to do this ( I would guess springtime)