This is not a good time to transplant this as it is (should be) in flower. The best time would be next autumn. Also, it has an extensive rootstock. If you can get it out complete then it should transplant OK but if the roots are entangled with other plants and get badly broken then the prospects are not so good.

Have a look around the base of the plant too.They usually set roots down from a low growing branch,so you could transplant these as well,though not until spring.It may be worth doing this as a well established jasmine would be very difficult to remove intact as Bulbaholic says.